Thread: Chinese remainder theorem

why there is not such number x in N:
x=2(mod6)
x=0(mod15)
x=4(mod7)

Originally Posted by cvcv49

why there is not such number x in N:
x=2(mod6)
x=0(mod15)
x=4(mod7)

If then is even, and if also then it must be an even multiple of 15. But even multiples of 15 are multiples of 6 so...

The CRT doesn't apply here since

Tonio

Originally Posted by cvcv49

why there is not such number x in N:
x=2(mod6)
x=0(mod15)
x=4(mod7)

Hint: the moduli must be pairwise relatively prime.