What is the digit in the ten's place of 23^(41)*25^(40)? How do you calculate this? The usual method for this kind of problem is using the Binomial theorem.

benatudq

benatudq

Answered question

2022-10-23

What is the digit in the ten's place of 23 41 25 40 ? How do you calculate this? The usual method for this kind of problem is using the Binomial theorem.

Answer & Explanation

DoryErrofbi

DoryErrofbi

Beginner2022-10-24Added 12 answers

Note that 25 2 = 625 25 mod 100, so that in fact 25 n 25 mod 100 for any n. Because ϕ ( 100 ) = 40, by Euler's theorem we have that a 40 1 mod 100 for any a relatively prime to 100 (as 23 is). Thus 23 41 23 mod 100. Now put these results together to find
23 41 25 40 mod 100.
Deborah Proctor

Deborah Proctor

Beginner2022-10-25Added 3 answers

On applying   a b mod a c =   a ( b mod c ) = mod Distributive Law we get
25 1 + J 23 1 + 2 K mod 100 = 25 ( 25 J 23 1 + 2 K   1 J ( 1 ) 1 + 2 K   3 mod 4 ) = 25 ( 3 )

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