8. Prove that n!+1 and (n+1)!+1 are integer n. relatively prime for every positive

Find all primes of the form 22" + 5, where n is a nonnegative integer.

Prove by mathematical induction that for all positive integers n > 1: a 12 x 2 + 2² × 3 + 3² × 4 + ·· . + n?(п + 1) n (n + 1) (п + 2) (Зп + 1) b 1 x 22 + 2 × 3² + 3 × 4² + ... + n(п + 1)? %3Dn (п + 1) (п + 2) (Зп + 5)

11. Prove that 31 (n³ +5n+6) for every integer n ≥ 0.