Menu Close

find-minimum-value-of-m-such-that-m-19-1800-mod-2029-

Tinku Tara 0 Comments
Pin




Question Number 197752 by cortano12 last updated on 27/Sep/23
find minimum value of m such that m^(19) = 1800 (mod 2029)
findminimumvalueofmsuchthatm19=1800(mod2029)
Answered by AST last updated on 27/Sep/23
m^(2028) =(m^(19) )^(107) m^(−5) ≡1(mod 2029) ⇒m^5 ≡(−229)^(107) ⇒m^5 ≡1183(mod 2029) m^(19) =(((m^5 )^4 )/m)≡1800(mod 2029) ⇒1800m≡(1183)^4 ≡1584(mod 2029) ⇒25m≡22(mod 2029) ⇒25m≡22+2029×7=2425=14225 ⇒m≡569(mod 2029) ⇒min{m}=569
m2028=(m19)107m−5≡1(mod2029)⇒m5≡(−229)107⇒m5≡1183(mod2029)m19=(m5)4m≡1800(mod2029)⇒1800m≡(1183)4≡1584(mod2029)⇒25m≡22(mod2029)⇒25m≡22+2029×7=2425=14225⇒m≡569(mod2029)⇒min{m}=569

Pin

Leave a Reply

Your email address will not be published. Required fields are marked *