Prove that 67n+ 17 cannot be a perfect square for any three consecutive integers n.

3

Prove that if n is a triangular number, then so are 9n + 1.25n + 3, and 49n + 6. Hint: Recall that in the formula for finding the n-th triangular number, the numerator is a product of two consecutive integers.

The average of five distinct integers is 65. If the largest integer is 75, what is the maximum possible value of the smallest integer? (A) 1 (B) 31 (C) (D) (E) 250

Prove using the following 1. Direct Proof: The sum of two even integers is also even 2. Indirect Proof: Show that if the square of an integer n is even, then n itself is even 3. By Contradiction: Show that if the square of an integer n is even, then n itself is even

3.2 (1) Factorised each of the expressions.