Suppose a,b,c,s,t are all integers, a 6=0,a∣b and a∣c . Then a∣(sb+tc) . Use it in a proof of the following: Prove that if a is a non- 0 integer, k∈Z,a∣(4k+3) , and a∣(2k+1) , then a=1 or a=−1 . Suggestion: use proof above and the fact that only divisors of 1 are 1 and -1 . 

Use proof by induction, prove that 2 divides 𝑛 2 + 𝑛 whenever n is a nonnegative integer

Proof Prove that e is irrational. [Hint: Assume that is rational (p and q are integers) and consider

Prove that if n is an integer and 7n+2 is even, then n is even. State which method you are using for the proof