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Using binomial theorem show that 1^99+2^99+3^99+4^99+5^99 is divisible by 5

Using binomial theorem show that 1^99+2^99+3^99+4^99+5^99 is divisible by 5

Grade:11

1 Answers

Harshit Singh
askIITians Faculty 5963 Points
2 years ago
Dear Student

We Know by divisibility rule thata^n+b^nis divisible bya+bwhennisodd.Since insertinga =−bthe value ofa^n+b^n=(−b)^n+b^n=0
For similar reason

1^99+4^99is divisible by1+4=5

Again2^99+3^99is divisible by2+3=5

And5^99is divisible by5

Hence the sum1^99+2^99+3^99+4^99+5^99must be divisible by 5


Thanks

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