
#1
Feb2612, 03:51 AM

P: 18

Find the smallest positive integer which when divided by 12, by 17, by 45 or by 70 gives
a remainder of 4 in each case. I know I can approach this problem by writing the equivalence classes. x=4mod12 x=4mod17 x=4mod45 or x=4mod70 I also know I can find x by multiplying 12*17*45 + 4, but this isn't the smallest positive integer. Can someone help me with a formula I can use? 



#2
Feb2612, 06:33 AM

HW Helper
P: 6,189

Erm... how about the solution x=4?
It is a solution and I don't think there are any smaller positive integers that are also a solution. 



#3
Feb2612, 01:32 PM

P: 144

If you for some reason do not like the number 4, you have to add the lcm of your moduli to get the next.



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