Discrete Mathematics

VENKATESH TK — Thu, 04 Apr 2013 07:56:24 +0200

Author(s): KRISHNARAM VENKATESH; PARASURAMAN DIVYA

Subject: Number Theory » Computational N.T.

This problem is identified while solving one of the unsolved problem exist currently. Problem name : Ghandhan Problem ------------------------------------------ M and N are integer and should satisfy following conditions. 1. M > N 2. M is not Divisible by N (Remainder not 0) 3. M*M is divisible by N. (Remainder is 0) 4. M and N are odd numbers. 5. N is not a multiple of any Square number.

There are solutions for below combinations. A) M and N are even numbers M = 6 , N = 4 M = 12, N = 8 i.e. N multiples of 4 whereas M multiples of 6. (4 is square number) B)M is even number and N is odd number M = 12, N = 9 M = 24, N = 18 i.e.N multiples of 9 whereas M multiples of 12. (9 is square number). C) M and N are odd number M = 15, N = 9 i.e. N is multiples of any square number (multiples of 3*3 here)

But need solution for odd number for both M and N with 5 conditions mentioned above ? Also need confirmation whether there are finite number of solutions exist for the same?

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Discrete Mathematics