Let m%3= i=1 where pi < p2 < ... < pi are prime numbers and a; 2 0 integers. Show that dE N is a divisor of m if and only d= [I p;* with c; an integer, such that 0 0 are integers then i=1 i=1 gcd(m, n) = I min(ai,bi). %3D i=1
Let m%3= i=1 where pi < p2 < ... < pi are prime numbers and a; 2 0 integers. Show that dE N is a divisor of m if and only d= [I p;* with c; an integer, such that 0 0 are integers then i=1 i=1 gcd(m, n) = I min(ai,bi). %3D i=1
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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Question
![3) Let
II
m =
i=1
where pi < p2 < ... < pi are prime numbers and a; 2 0 integers. Show
that deN is a divisor of m if and only d = [I p' with c; an integer, such
i=1
that 0<c; < a; for all 1<i<l.
Conclude from this that if n = II p", where b; > 0 are integers then
П
i=1
min(ai,bi)
gcd(m, n)
i=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F001eda53-19f3-49af-8959-1aa5b0b6fb9b%2F7470a18d-4231-42a6-a389-c743e1ca6a8e%2Fw5xj4brk_processed.png&w=3840&q=75)
Transcribed Image Text:3) Let
II
m =
i=1
where pi < p2 < ... < pi are prime numbers and a; 2 0 integers. Show
that deN is a divisor of m if and only d = [I p' with c; an integer, such
i=1
that 0<c; < a; for all 1<i<l.
Conclude from this that if n = II p", where b; > 0 are integers then
П
i=1
min(ai,bi)
gcd(m, n)
i=1
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