1. ## Chinese remainder theorem

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

2. Originally Posted by cvcv49
why there is not such number x in N:
x=2(mod6)
x=0(mod15)
x=4(mod7)

If $x=2\!\!\!\pmod 6$ then $x$ is even, and if also $x=0\!\!\!\pmod {15}$ 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 $gcd(6,15)\neq 1$

Tonio

3. 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.