a: With justification, find an inverse for 3276 modulo 3025.
b: With justification, find an inverse for 3276 modulo 3026.
I am completely stumped
How can there be a positive integer 's' such that 3276 ∙ s ≡ 1 (mod 3025 (or 3026)) ???
Hello, starman_dx!
There are a number of streamlined procedures.
I'll show you a primitive algebraic approach.
We have: .(a) With justification, find an inverse for 3276 modulo 3025.
This means: .
Solve for
Since is an integer, is a multiple of 3025.
. . That is: .
Solve for .[1]
Since is an integer, is a multiple of 251.
. . That is: .
Solve for .[2]
Since is an integer, is a multiple of 13.
. . That is: .
Solve for .[3]
We see that is first an integer when
Substitute into [3]: .
Substitute into [2]: .
Substitute into [1]: .
Therefore, the inverse of is: .
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