# 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:

$A=1069 \ \\ B=326 \ \\ C=A \cdot \ B=1069 \cdot \ 326=348494 \ \\ x=C - 3 \cdot \ \lfloor C/3 \rfloor=348494 - 3 \cdot \ \lfloor 348494/3 \rfloor=2 \ \\ A=6n+1 \ \\ B=3m+2 \ \\ C=A \cdot \ B=(6n+1)(3m+2)=18mn+3m+12n+2=3(6mn+m+4n)+2$

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