Question 67

For two positive integers a and b, if $$(a + b)^{(a + b)}$$ is divisible by 500, then the least possible value of a $$\times$$ b is:

Solution

If $$(a + b)^{(a + b)}$$ is divisible by 500,

$$500 = 2^2 \times 5^3$$

=> Least value of $$a + b = 2 \times 5 = 10$$

For least $$a$$ and $$b$$, let $$a = 1$$

=> $$b = 10 - 1 = 9$$

$$\therefore$$ Min $$(a \times b) = 1 \times 9 = 9$$

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