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# Modular equations

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Find the smallest positive N and M that will satisfy the following two modular equations:

111,119 mod N =954 and 111,119 mod M = 82. Thanks for any help.

Guest Nov 10, 2017
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#1
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The "mod" value is the remainder after division.

To find N in the equation:  111,119 mod N = 954

first, subtract 954 from 111,119     --->     111,119 - 954  =  110,165

now, find the factors of 110,165     --->     110,165  =  5 x 11 x 2003

we need a factor larger than 954     --->     N = 2003

To find M in the equation:  111,119 mod M = 82

first, subtract 82 from 111,119     --->     111,119 - 82  =  111,037

now, find the factors of 111,037      --->     111,037  =  37 x 3001

we need a factor larger than 82     --->     M = 3001

geno3141  Nov 10, 2017
#2
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Thank you geno3141.

Guest Nov 10, 2017

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