For-p-q-and-r-prime-numbers-satisfying-p-q-1-r-1-1064-r-p-1-q-1-1554-find-the-value-p-q-1-r-

Question Number 213463 by golsendro last updated on 06/Nov/24

For p, q and r prime numbers

satisfying {\begin{cases} p (q + 1) (r + 1) = 1064 \\ r (p + 1) (q + 1) = 1554 \end{cases}

find the value p (q + 1) r

Answered by A5T last updated on 06/Nov/24

p ∣ 1064 = 2^{3} \times 7 \times 19; p + 1 ∣ 1554 = 2 \times 3 \times 7 \times 37

\Rightarrow p = 2 \Rightarrow (q + 1) (r + 1) = 532 = 4 \times 7 \times 19

\Rightarrow r (q + 1) = 2 \times 7 \times 37 \Rightarrow r = 37 \Rightarrow q = 13

\Rightarrow p (q + 1) r = 2 \times 14 \times 37 = 1036

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