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Theorems for Continuity

Prove that ...

Question

Prove that $(106)^{85} - (85)^{106}$ is divided by 3 ?

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Solution

$L . H . S . = (1 + 105)^{85} - (1 + 84)^{106}$
1,1 will cancel and both 105 and 84 are divisible by 3 and binomial coefficients which occur are all integers and hence L.H.S. is divisible by 3.

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