Question 6
Two primes $$p,q$$ are such that $$p+q$$ is odd and $$q-10p=23$$. Then $$q-20p$$ equals
Solution
Since the sum of two primes is odd, one of the primes must be $$2$$. The equation $$q-10p=23$$ cannot hold with $$q=2$$, so $$p=2$$ and $$q=43$$. Therefore $$q-20p=43-40=3$$.
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