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If N and x are positive integers such that NN = 2160 and N2 + 2N is an integral multiple of 2x, then the largest possible x is

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Calculation:

NN = 2160 = 25 × 32

⇒ (25)32

⇒ (32)32; which is in form of NN

⇒ N2+ 2N = 322 + 232

⇒ (25)2 + 232

⇒ 210 + 232

⇒ 210(1 + 222)

⇒ N2+ 2N = 210(1 + 222)

⇒ Clearly, N2+ 2N is an integral multiple of 210 which is in form of 2x

∴ Largest possible value of x = 10

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