Modular arithmetic
is a prime number, the remainder is 9 when is divided by 10. Find the value of .
The answer is 5.
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1 solution
Given that, p^2 +2014=9(mod 10) So,p^2= -2005= -2005+203 * 10=25(mod 10) and finally p=5(mod 10).Now we can write p in the form, p=10k+5 where k is a subset of the set of natural number.It is very clear that p will be a prime if and only if k=0 otherwise p will be divided by 5.So the only solution is p=10 * 0+5=5