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Let m = p₁¹p²²ª...p"² and n = p₁¹p2...pt where p₁,..., Ps are distinct prime numbers ans ri, ti ≥ 0 for all i € {1,..., s}. Prove the following: i) (m, n) = p¹p²...p" where u₂ = min({ri, ti}) for all i = {1,..., s} ii) [m, n] = pp...ps where v₂ = max({ri, ti}) for all i € {1,..., s}.

Let m = p₁¹p²²ª...p"² and n = p₁¹p2...pt where p₁,..., Ps are distinct prime numbers ans ri, ti ≥ 0 for all i € {1,..., s}. Prove the following: i) (m, n) = p¹p²...p" where u₂ = min({ri, ti}) for all i = {1,..., s} ii) [m, n] = pp...ps where v₂ = max({ri, ti}) for all i € {1,..., s}.

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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Let m= pp...ps and n = = pp2...pt where p₁,..., Ps are distinct prime numbers ans ri, ti ≥0 for all i = {1,..., s}. Prove the following: i) (m, n) = p¹p2...p" where u = min({ri, ti}) for all i = {1,..., s} ii) [m, n] = p¹p²...ps where v₁ = max({ri, ti}) for all i = {1,..., s}.
Transcribed Image Text:Let m= pp...ps and n = = pp2...pt where p₁,..., Ps are distinct prime numbers ans ri, ti ≥0 for all i = {1,..., s}. Prove the following: i) (m, n) = p¹p2...p" where u = min({ri, ti}) for all i = {1,..., s} ii) [m, n] = p¹p²...ps where v₁ = max({ri, ti}) for all i = {1,..., s}.
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