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Question Number 71852 by Rio Michael last updated on 21/Oct/19
show that 5^(22) + 17^(22) ≡ 6 (mod 11)
showthat522+1722≡6(mod11)
Answered by mind is power last updated on 21/Oct/19
ferma little theorem since 11 is prime⇒5^(10) =1(11)⇒5^(20) =1^2 =1(11) 5^(22) =25(11)=3(11) 17=6(11)⇒17^(20) =6^(20) =1(11) ⇒7^(22) =6^2 (11)=3(11) ⇒7^(22) +5^(22) =3+3(11)=6(11)
fermalittletheoremsince11isprime⇒510=1(11)⇒520=12=1(11)522=25(11)=3(11)17=6(11)⇒1720=620=1(11)⇒722=62(11)=3(11)⇒722+522=3+3(11)=6(11)
Commented by Rio Michael last updated on 21/Oct/19
thanks
thanks

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