Remainder

A is an arbitrary integer that gives remainder 1 in the division with 6. B is an arbitrary integer that gives remainder 2 the division by. What makes remainder in division by 3 product of numbers A x B ?

Correct result:

x =  2

Solution:

A=1069 B=326 C=A⋅ B=1069⋅ 326=348494 x=C−3⋅ ⌊C/3⌋=348494−3⋅ ⌊348494/3⌋=2 A=6n+1 B=3m+2 C=A⋅ B=(6n+1)(3m+2)=18mn+3m+12n+2=3(6mn+m+4n)+2

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