Happy CNY! and we have CRT!
A natural number has remainder when divided by , gives remainder when divided by , and has remainder when divided by .
What is the least possible value of ?
Feel free to post your own creative solution! Happy Chinese New Year!
The answer is 368.
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1 solution
My solution.
X = 3 mod 5
X = 4 mod 7
X = 5 mod 11
N=5×7×11=385
n1=7×11=77
n2=5×11=55
n3=5×7=35
77y = 1 mod 5
y=3
55y = 1 mod 7
y=6
35y = 1 mod 11
y=6
X0 = 3×77×3 + 6×55×4 + 6×35×5 = 693 + 1320 + 1050 = 3063
3063 = 368 mod 385
Xn = 368 + 385k
X0 = 368