Consider the following statements: 1. If (3m³ + 2m² + 5m + n)/m is not an integer, where m and n are integers, then n is not divisible by m. 2. 5(8^m) + 2^(3m) is divisible by 48 for all whole numbers m. Which of the statements given above is/are correct ?

Statement 1: (3m³ + 2m² + 5m + n)/m = 3m² + 2m + 5 + n/m. The first three terms are integers. So the whole expression is integer iff n/m is integer, i.e., m divides n. Contrapositive: if expression is not integer, then m does not divide n. So statement 1 is correct. Statement 2: 5(8^m) + 2^(3m) = 5·8^m + 8^m = 6·8^m. For m = 0: 6·1 = 6, not divisible by 48. So statement 2 is false. Only statement 1 is correct.