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
- 2
- 3
- 5
- 4
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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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
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