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I have a problem to define a set of natural numbers that meet the following equation:

m^{2}+1[itex]\equiv[/itex]0[5]

I have found that a set of this equation is : {2,3,7,8}+k*10, k[itex]\in[/itex]N

i.e: k= {0,1,2,3,...........,n}

example: (2+(0*10)^{2})+1=5

(3+(1*10)^{2})+1=13^{2}+1=170

Result:m=[2+k*10; 3+k*10; 7+k*10; 8+k*10]

How can I describe this result logically in mathematics ?

Thanks.

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# Arithmetics in Z

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