Question 144

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

Solution

$$55^3 + 17^3 - 72^3$$ = $$(55-72)k + 17^3$$. This is divisible by 17

Remainder when $$55^3$$ is divided by 3 = 1

Remainder when $$17^3$$ is divided by 3 = -1

Remainder when $$72^3$$ is divided by 3 = 0

So, $$55^3 + 17^3 - 72^3$$ is divisible by 3

So, the answer is d) 3 and 17