Q4 REMAINDERS

Let N=55^3 +17^3-72^3. N is divisible by

a. both 7 and 13

b. both 3 and 13

c. both 17 and 7

N=55^3+17^3−72^3=(54+1)^3+(18−1)^3−72^3

=(51+4)^3+17^3−(68+4)^3.

These two different forms of the expression are divisible by 3 and 17 both.

Elimination strategy:

Check the divisibility by 13, it is seen that it is not divisible,

now check for 3, it is divisible, hence the only option will be (d)

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