An algebra problem by Aaryan Maheshwari

Algebra Level 3

Let X = 3 2 2 × 3 3 4 × 3 5 6 × 3 6 8 . X=32^2\times33^4\times35^6\times36^8. If X X is a multiple of 3 4 n 34^n where n n is a non-negative integer, then find the value of n 34 − 3 4 n . n^{34}-34^n.


The answer is -1.

Aaryan Maheshwari by Aaryan Maheshwari , 16, India

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1 solution

Kb E
Dec 26, 2017

n = 0 n=0 (because 17 is a factor of 34 but not 3 2 2 × 3 3 4 × 3 5 6 × 3 6 8 32^2\times33^4\times35^6\times36^8 ) So, 0 34 − 3 4 0 = − 1 0^{34}-34^0 = -1

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