MediaWiki API result
This is the HTML representation of the JSON format. HTML is good for debugging, but is unsuitable for application use.
Specify the format parameter to change the output format. To see the non-HTML representation of the JSON format, set format=json.
See the complete documentation, or the API help for more information.
{
"batchcomplete": "",
"continue": {
"lecontinue": "20250916033521|3301",
"continue": "-||"
},
"query": {
"logevents": [
{
"logid": 3311,
"ns": 0,
"title": "E:16892",
"pageid": 3104,
"logpage": 3104,
"revid": 10785,
"params": {},
"type": "create",
"action": "create",
"user": "Andrei.Horvat",
"timestamp": "2025-09-20T13:32:32Z",
"comment": "Created page with \"'''[[E:16892]] (Nicolae Mu\u0219uroia)''' ''Afla\u021bi suma divizorilor pari ai celui mai mare num\u0103r natural <math>a</math>, cu <math>a<1000</math>, pentru care suma divizorilor impari este egal\u0103 cu <math>24</math>.'' '''Solu\u021bie''' C\u0103ut\u0103m numere de trei cifre, de forma <math>2^m \\cdot b</math>, cu <math>m\\in \\mathbb{N}^\\ast</math> \u0219i <math>b</math>, unde suma divizorilor num\u0103rului natural impar <math>b</math> este egal\u0103 cu <math>24</math>. Avem dou\u0103 posibilit\u0103\u021bi...\""
},
{
"logid": 3310,
"ns": 0,
"title": "E:16893",
"pageid": 3103,
"logpage": 3103,
"revid": 10781,
"params": {},
"type": "create",
"action": "create",
"user": "Andrei.Horvat",
"timestamp": "2025-09-20T13:12:15Z",
"comment": "Created page with \"'''[[E:16893]] (Traian Covaciu)''' ''Ar\u0103ta\u021bi c\u0103 numerele <math>7n-1</math> \u0219i <math>17n-1</math> sunt simultan prime doar dac\u0103 <math>n</math> este un multiplu natural al lui <math>6</math>.'' '''Solu\u021bie''' Pentru <math>n=6</math> se ob\u021bin numerele prime <math>42</math> \u0219i <math>101</math>. Dac\u0103 <math>n</math> este impar, atunci numerele <math>7n-1</math> \u0219i <math>17n-1</math> sunt pare, deci nu pot fi prime, ceea ce implic\u0103 faptul c\u0103 <math>2 |\\, n</math>....\""
},
{
"logid": 3309,
"ns": 0,
"title": "E:16891",
"pageid": 3102,
"logpage": 3102,
"revid": 10778,
"params": {},
"type": "create",
"action": "create",
"user": "Andrei.Horvat",
"timestamp": "2025-09-20T12:58:44Z",
"comment": "Created page with \"'''[[E:16891]] (Sever Pop)''' ''Determina\u021bi numerele prime <math>p</math>, <math>q</math>, <math>r</math>, distincte dou\u0103 c\u00e2te dou\u0103, pentru care are loc egalitatea <math>3p^4 - 5q^4 - 4r^2 = 26</math>.'' '''Solu\u021bie''' ''Deoarece <math>3p^4 - 5q^4=2\\left(13+2r^2\\right)</math> este num\u0103r par, deducem c\u0103 numerele prime <math>p</math> \u0219i <math>q</math> au aceea\u0219i paritate, deci sunt impare. Cum <math>3p^4 - 5q^4>26>0</math>, avem <math>3p^3>5q^4</math>, deci <ma...\""
},
{
"logid": 3308,
"ns": 0,
"title": "E:16889",
"pageid": 3101,
"logpage": 3101,
"revid": 10775,
"params": {},
"type": "create",
"action": "create",
"user": "Andrei.Horvat",
"timestamp": "2025-09-20T05:42:38Z",
"comment": "Created page with \"'''[[E:16889]] (C\u0103lin Hossu)''' ''Prin \u00eemp\u0103r\u021birea unui num\u0103r de patru cifre la r\u0103sturnatul s\u0103u, se ob\u021bine c\u00e2tul <math>2</math> \u0219i restul <math>1977</math>. Afla\u021bi num\u0103rul, \u0219tiind c\u0103 diferen\u021ba dintre cifra miilor \u0219i cifra unit\u0103\u021bilor este <math>5</math>, iar cifra sutelor este cu <math>4</math> mai mare dec\u00e2t cifra zecilor.'' '''Solu\u021bie'''\""
},
{
"logid": 3307,
"ns": 0,
"title": "E:16890",
"pageid": 3100,
"logpage": 3100,
"revid": 10772,
"params": {},
"type": "create",
"action": "create",
"user": "Andrei.Horvat",
"timestamp": "2025-09-20T05:36:12Z",
"comment": "Created page with \"'''[[E:16890]] (Bogdan Zetea, C\u0103lin Hossu)''' ''Demonstra\u021bi c\u0103, pentru orice num\u0103r natural nenul <math>n</math>, num\u0103rul <math>2024^n+n^{2024} + 2</math> nu este un p\u0103trat perfect.'' '''Solu\u021bie''' Fie <math>N = 2024^n+n^{2024} + 2</math>. Dac\u0103 <math>n</math> este un num\u0103r par, atunci exist\u0103 numerele naturale nenule <math>t</math> \u0219i <math>u</math> pentru care <math>n^{2024} = 4t</math> \u0219i <math>2024^n = 4u</math>. Atunci <math>N = 4t+4u+2 <math>, deci exi...\""
},
{
"logid": 3306,
"ns": 0,
"title": "E:16888",
"pageid": 3099,
"logpage": 3099,
"revid": 10767,
"params": {},
"type": "create",
"action": "create",
"user": "Andrei.Horvat",
"timestamp": "2025-09-19T19:32:21Z",
"comment": "Created page with \"'''[[E:16888]] (Gheorghe Boroica)''' ''Consider\u0103m <math>n<math> un num\u0103r natural nenul. Demonstra\u021bi c\u0103 num\u0103rul <math>N = \\underbrace{44\\ldots4}_{n \\text{ cifre}}\\underbrace{22\\ldots2}_{n \\text{ cifre}} </math> poate fi scris ca produsul a dou\u0103 numere naturale consecutive.'' ''''Solu\u021bie''' Dac\u0103 <math>a=\\underbrace{11\\ldots1}_{n \\text{ cifre}}</math>, atunci <math>9\\cdot a+1=10^n</math> \u0219i <math display=\"block\">N= 4\\cdot a \\cdot 10^n + 2 \\cdot a = 2\\cdot a \\...\""
},
{
"logid": 3305,
"ns": 0,
"title": "E:16887",
"pageid": 3098,
"logpage": 3098,
"revid": 10765,
"params": {},
"type": "create",
"action": "create",
"user": "Andrei.Horvat",
"timestamp": "2025-09-19T19:29:49Z",
"comment": "Created page with \"'''[[E:16887]] (Gheorghe Boroica)''' ''Suma a <math>90</math> de numere naturale este <math>2069</math>. Ar\u0103ta\u021bi c\u0103 exist\u0103, printre acestea, cel pu\u021bin trei numere egale.'' '''Solu\u021bie''' Fie <math>S</math> suma celor <math>90</math> de numere. Presupunem contrariul, deci printre cele <math>90</math> de numere, cel mult dou\u0103 numere pot fi egale. Atunci <math display=\"block\"> \tS \\ge \\left(1+1\\right) + \\left(2+2\\right) + \\left(3+3\\right)+\\ldots +\\left(45+45\\right...\""
},
{
"logid": 3304,
"ns": 0,
"title": "P:1800",
"pageid": 3097,
"logpage": 3097,
"revid": 10761,
"params": {},
"type": "create",
"action": "create",
"user": "Andrei.Horvat",
"timestamp": "2025-09-19T16:57:10Z",
"comment": "Created page with \"'''[[P:1800]] (Ioan Ovidiu Pop, Coroieni)''' ''Afla\u021bi num\u0103rul de telefon <math>\\overline{07abcdefgh}</math>, format din zece cifre, nu neap\u0103rat distincte, pentru care numerele <math>a+c</math>, <math>b+c</math>, <math>d+e</math>, <math>c+d</math>, <math>a+b+e</math>, <math>c+d+f</math>, <math>b+c+g</math> \u0219i <math>d+e+h</math> sunt opt numere consecutive a\u0219ezate \u00een ordine cresc\u0103toare.'' '''Solu\u021bie''' Cele opt numere consecutive a\u0219ezate \u00een ordine cresc\u0103toare...\""
},
{
"logid": 3303,
"ns": 0,
"title": "23964",
"pageid": 3096,
"logpage": 3096,
"revid": 10758,
"params": {},
"type": "create",
"action": "create",
"user": "Andrei.Horvat",
"timestamp": "2025-09-17T17:50:42Z",
"comment": "Created page with \"'''[[23964]] (Marin Banco\u0219)''' ''S\u0103 de demonstreze inegalitatea <math display=\"block\"> \\sum_{i=2}^{n} \\sqrt[i]{\\left(i!\\right)^2} < \\frac{2n^3+9n^2+13n-24}{24} .</math>'' '''Solu\u021bie''' Pentru orice num\u0103r natural <math>n</math>, cu <math> n\\ge 2</math> are loc inegalitatea <math display=\"block\"> \\sqrt[n]{n!} = \\sqrt[n]{1\\cdot 2\\cdot \\ldots \\cdot n} < \\frac{1+2+\\ldots+n}{n} = \\frac{n+1}{2}.</math> Atunci <math display=\"block\"> \\sum_{i=2}^{n} \\sqrt[i]{\\left(I!\\right)...\""
},
{
"logid": 3302,
"ns": 0,
"title": "Gazeta matematic\u0103 1998",
"pageid": 3095,
"logpage": 3095,
"revid": 10754,
"params": {},
"type": "create",
"action": "create",
"user": "Andrei.Horvat",
"timestamp": "2025-09-17T17:48:23Z",
"comment": "Created page with \"== Gazeta Matematic\u0103 9/1998 ==\""
}
]
}
}