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Numbers with exactly three divisors are squares of primes

This type of question, asked 2 times: 3 Feb 2022 Tier II, 18 Jan 2026 Tier II. All 2 questions below, oldest first.

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  1. Question 1

    3 Feb 2022 Tier II

    61
    Let p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself. If q>pq > p and both are two-digit numbers, and r>sr > s and both are one-digit numbers, then the value of the expression p−q−1r−s\frac{p - q - 1}{r - s} is:

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  2. Question 2

    18 Jan 2026 Tier II

    26
    How many integers in the set {1,2,3……,100}\{1, 2, 3\ldots\ldots, 100\} have exactly 3 divisors?

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