Study the following claim as well as the "proof": claim. for all n e n, 3 | (n3+ 44n). "proof". when n 1, n3 +44n = 45 is divisible by 3. when n -2, n3 +44n = 96 3, n + 44n = 1004400 is divisible by 3. thus 3 | (n3 7 159 is divisible by 3. whenn= 100, 44n) for all n e n. is divisible by 3. when n = ns +44n 3 complete the following questions concerning the above claim and "proof" (1) determine whether the "proof" is rigorous. identify the issues in the "proof" if any (2) determine whether the claim is true or false. justify the answer in part (3). (3) if the the claim is true and the "proof" is not rigorous, then provide rigorous proof. if the claim is false, give a correct and a concrete counterexample. instructed. if the claim is false, then (obviously) there is no hint. complete the parts way the "proof" could be correct. as