Chinese remainder theorem

[cvcv49]

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

 

[jk22]

Hello, nice to meet you. I'm new to this forum.

If we take the 2 1st line :

x=2+6m
x=15n

m,n are integers

we sub and get : 2=-6m-15n=3(-2m-5n)

which is impossible since 2 is not a multiple of 3.