Question 1207720
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Find the number of solutions to 
N = {2 mod 5},
N = {2 mod 6},
N = {2 mod 7}.
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<pre>
Consider the number N-2.


   N-2 = {0 mod 5},

   N-2 = {0 mod 6} 

and

   N-2 = {0 mod 7}.


It means that N-2 is a multiple of 5, 6 and 7, at the same time.


The integer numbers  N-2  in the interval  [-2,998]  divisible by 5, 6 and 7  
at the same time are those multiple of 210,  i.e. 0, 210, 420, 630, 840.

Hence, the solutions N under the problem's question are the numbers 2, 212, 422,  632, 842.    


In all, there are 5 solutions.    <U>ANSWER</U>
</pre>

Solved.