Suppose that n is a positive integer such that (n − 1)! -1 (mod n) and (n-1)! #0 (mod n) Find the largest possible value of n or enter 999 if there are infinitely many such positive integers. Type your answer... Find the least residue of the (multiplicative) inverse of modulo 467. (Note that 467 is prime.) Type your answer... (467-10)!

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter2: Working With Real Numbers
Section2.7: Problem Solving: Consecutive Integers
Problem 14OE
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Need help with these two Intro to Elementary Number Theory Homework problems.

 

Suppose that n is a positive integer such that
(n − 1)! -1 (mod n) and
(n-1)! #0 (mod n)
Find the largest possible value of n or enter 999 if there are infinitely many such positive integers.
Type your answer...
Transcribed Image Text:Suppose that n is a positive integer such that (n − 1)! -1 (mod n) and (n-1)! #0 (mod n) Find the largest possible value of n or enter 999 if there are infinitely many such positive integers. Type your answer...
Find the least residue of the (multiplicative) inverse of
modulo 467. (Note that 467 is prime.)
Type your answer...
(467-10)!
Transcribed Image Text:Find the least residue of the (multiplicative) inverse of modulo 467. (Note that 467 is prime.) Type your answer... (467-10)!
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