Find the minimum number
If a positive integer is divided by 7 and remainder will get 1, and that number also divided by 5 and remainder will get 2. Find the least value of .
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1 solution
let x is the number. a is the quotient of 7 and b is the quotient of 5 7a+1=x 5b+2=x 7a+1=5b+2
7a-5b=1 take a=1 , b=1 ---> 7 - 5 = 1 not satisfy take a=2 , b=2 ---> 14 - 10 = 1 not satisfy take a=3 , b=3 ---> 21 - 15 = 1 not satisfy take a=3 , b=4 ---> 21 - 20 = 1 Satisfied
so a=3 , b=4 So the output is x=7*3 + 1 = 22