True or false? In each case, give a proof or provide a counterexample that disproves the g...

True or false? In each case, give a proof or provide a counterexample that disproves the given statement.

(a) [BB] 5n −4− n + 1 is divisible by 7 for all n ≥ 1.

(b) for all n ≥ 1.

(c) If n ≥ 2, gcd

(d) (For students of calculus) n15 ≥ 2n for all n ≥ 1.