JEE MainMathematicsToughPermutations and Combinations

n is selected from the set and the number
2^n + 3^n + 5^n is formed. Total number of ways of selecting n so
that the formed number is divisible by 4 is equal to

Show answer and solution

If n is odd.

3^{n} = 4\lambda_{1} - 1,5^{n} = 4\lambda_{2} + 1

\Rightarrow

2^n + 3^n + 5^n is divisible by 4 if n > 2
Thus, n = 3, 5, 7, 9.....

Source: Grass-G / M-23 Mathematics Paper 31 Dec FST.docx

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