Diophantine Equation on Powers and Factorials | Singapore Mathematical Olympiad 2008

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Комментарии
Автор

Actually, n!≡-1(mod (n+1))
So by Wilson’s Theorem
Yes, (n+1) is prime

applealvin
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Does this not fit using mathematical induction? Might be exactly on that way. I mean proving the left with the right side. I got the way but ... seems not true. No offense. :)

marlongrau
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Hi can you solve this problem. Suppose a, b, c, z are nonzero complex numbers such that |a|=|b|=|c|, |z|=1 and az^2+bz+c=0. Show that b^2=ac.

bartekabuz
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Wait just because p prime divided n plus 1 does not tell you for certain it divides n! plus 1...

leif
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Can't we just use converse Wilson s theorem to get n+1 is prime?

advaykumar
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Nice, how did you get to considering n^2 ?

tomask
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i did it different way, that probably is easier to invent- but also it is much longer solution than yours, therefore i like yours more :)

Szynkaa
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all of the questions can be solved by just throwing in some dummy numbers, like -1, 0, 1, 2, 3, but I just do not know how to prove that these are the only solutions :(

tianqilong