Let-p-P-and-m-Z-Find-p-m-such-that-p-m-1-p-1-146410-

Question Number 4199 by Yozzii last updated on 01/Jan/16

L e t p \in P a n d m \in Z^{+} .

F i n d (p, m) s u c h t h a t p^{m - 1} (p - 1) = 146410 .

Answered by Rasheed Soomro last updated on 01/Jan/16

p^{m - 1} (p - 1) = 146410

146410 = 2 \times 5 \times 11^{4}

p \in P \Rightarrow p = 2 ∣ p i s o d d

F o r p = 2, 146410 s h o u l d b e o f 2^{n} t y p e b u t i t

{i s n}^{'} t .

∴ p i s o d d

∴ p - 1 i s e v e n

e v e n f a c t o r s o f 146410 a r e 2, 10, 22

p - 1 = 2, 10, 22 \Rightarrow p = 3, 11, 23

∵ 3 a n d 23 a r e n o t f a c t o r s

∴ p = 11

11^{m - 1} (11 - 1) = 146410

11^{m - 1} = 11^{4}

m - 1 = 4

m = 5

(p, m) = (11, 5)