Question

Let A be the largest positive integer that divides all the numbers of the form\( (2^{k}+3^{k}+5^{k})\) and B be the largest positive integer that divides all the numbers of the form \((3^{k}+4^{k}+5^{k}) \), where k is any positive integer. Then (A + B) equals

• A. 2
• B. 3
• C. 5
• D. 4

Answer 1

The Correct Option is D

A:
For k = 1, the expression is 2 + 3 + 5 = 10.

For k = 2, the expression is 4 + 9 + 25 = 38.

For k = 3, the expression is 8 + 27 + 125 = 160.

We observe that 2 is a common factor for all these expressions.

B:
For k = 1, the expression is 3 + 4 + 5 = 12.

For k = 2, the expression is 9 + 16 + 25 = 50.

For k = 3, the expression is 27 + 64 + 125 = 216.

We observe that 2 is a common factor for all these expressions.

Therefore, A = 2 and B = 2.

Hence, A + B = 2 + 2 = 4.