My Math Forum ((my) mod n ) congruent to n-1

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 January 28th, 2012, 07:34 PM #1 Member   Joined: Apr 2010 Posts: 34 Thanks: 0 ((my) mod n ) congruent to n-1 If given a 'n' value and m = floor ( squareroot(n) ) then is there any way to find the value of 'y' , such that ((m*y) mod n) is congruent to (n-1)
 January 28th, 2012, 09:02 PM #2 Member   Joined: Apr 2010 Posts: 34 Thanks: 0 Re: ((my) mod n ) congruent to n-1 with the help of a friend i figured out that, if m is the divisor of n, it wont be possible to get a solution . But what about the other values?
 January 28th, 2012, 10:07 PM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: ((my) mod n ) congruent to n-1 I think what you're saying is, given m and $n=\lfloor\sqrt m\rfloor,$ you want to find y such that $my\equiv n-1\pmod n.$ Is that right?
January 28th, 2012, 10:19 PM   #4
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Re: ((my) mod n ) congruent to n-1

Quote:
 Originally Posted by CRGreathouse I think what you're saying is, given m and $n=\lfloor\sqrt m\rfloor,$ you want to find y such that $my\equiv n-1\pmod n.$ Is that right?
it's $m=\lfloor\sqrt n\rfloor,$ and $my\equiv n-1\pmod n.$
I found that modular inverse would yield the answer . But it gives only the smallest modular number. To get the number i require it has long way to go from smallest number.

 January 28th, 2012, 10:21 PM #5 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: ((my) mod n ) congruent to n-1 The modular inverse gives all the answers. To get from one to the next you add the modulus.

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