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3) Let II" , m i=1 where p1 < p2 < ... < pi are prime numbers and a; > 0 integers. Show that d eN is a divisor of m if and only d = II p§ª with c; an integer, such i=1 that 0 < c; < a; for all 1 < i 0 are integers then %3D i=1 min(a;,b¿) gcd(m, п) i=1

3) Let II" , m i=1 where p1 < p2 < ... < pi are prime numbers and a; > 0 integers. Show that d eN is a divisor of m if and only d = II p§ª with c; an integer, such i=1 that 0 < c; < a; for all 1 < i 0 are integers then %3D i=1 min(a;,b¿) gcd(m, п) i=1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3) Let m = i=1 where pi < p2 < ... < pi are prime numbers and a; > 0 integers. Show that d e N is a divisor of m if and only d = II p* with c; an integer, such i=1 that 0 < c; < a; for all 1 < i <1. Conclude from this that ifn = [I p?', where b; > 0 are integers then i=1 ged(m, n) = I[p" min(a;,b;) Pi i=1
Transcribed Image Text:3) Let m = i=1 where pi < p2 < ... < pi are prime numbers and a; > 0 integers. Show that d e N is a divisor of m if and only d = II p* with c; an integer, such i=1 that 0 < c; < a; for all 1 < i <1. Conclude from this that ifn = [I p?', where b; > 0 are integers then i=1 ged(m, n) = I[p" min(a;,b;) Pi i=1
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