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
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
Updated On: Aug 21, 2024
- 2
- 3
- 5
- 4
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The Correct Option is D
Solution and Explanation
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.
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