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n is selected from the set {1,2,3,....,100} and the number 2^n+3^n+5^n is formed. Total number of ways of selecting n so that the number formed is divisible by 4 is

n is selected from the set {1,2,3,....,100} and the number 2^n+3^n+5^n is formed. Total number of ways of selecting n so that the number formed is divisible by 4 is

Grade:11

1 Answers

mycroft holmes
272 Points
7 years ago
If n is an odd number >1, then you have 3n+5n is divisible by 3+5=8, and so its easy to see that the expression is divisible by 4. If n is even, then the expression is of the form 4k+2.
 
So, the odd nrs from 3 to 99 inclusive, are the n to be chosen – so 49 choices of n.

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