1) Prove that no integer in the sequence 11, 111, 1111, 11111... is a perfect square.
2) If n is an odd integer, show that n^4 +4n^2 +11 is of the form 16k.
3) By using the division alogirthm, show
(i) if a and b are odd integers, then 8|(a^2-b^2)
(ii)if p>3 is a prime, then 24|(p^2-1)
(iii) for n>1, prove that n(n+1)(2n+1)/6 is an integer.
4) Find the largest integer n such that n is a divisor of a^5-a for all integers a.
2006-08-13
01:38:17
·
5 answers
·
asked by
edwinvandesar
1