Patrat perfect

lixandruandrey · Mesaj de **lixandruandrey** » 03 Aug 2014, 13:45

Fie a= 1x2x3x4x.....x n+57.
Determinati nâN, pentru care "a" este patrat perfect.

tata2008 · Mesaj de **tata2008** » 04 Aug 2014, 07:15

lixandruandrey scrie:Fie a= 1x2x3x4x.....x n+57.
Determinati nâN, pentru care "a" este patrat perfect.

$\rm{\bl\\ a =\underbrace{1x2x3x4x...xn}_{n!}+57= n!+57 =p.p \\ deci: \|a=\{64;81;100;121;144;169;...\} si\\ n=3 avem 3 ! = 6 \ne 64-57=7 fals , deci n\ne3;\\ n=4 avem 4! = 24=81-57=24 adev\breve{a}rat \rightarrow \fbox{n=4} ;\\ s.a.m.d.$

lixandruandrey · Mesaj de **lixandruandrey** » 06 Aug 2014, 11:55

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