Question

For which positive integer n, 2^8+2^15+2^n is a perfect square?

Answer 1

yes it is a perfect square because 2^8=2*2*2*2*2*2*2*2=256 when we take √256=16 so it is a perfect square

Answer 2

Answer:

16

Step-by-step explanation:

The value of n has to be determined such that 2^8+2^11+2^n is a perfect square.

2^8+2^11+2^n

= 2304 + 2^n

= 9*256 + 2^n

= 9*2^8 + 2^n

= 2^8*(9 + 2^(n-8))

If this is a perfect square, 9 + 2^(n-8) has to be a square.

The Pythagorean triplet (3, 4, 5) gives 9 + 16 = 25

2^(n-8) = 16

therefore answer is 16

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