Which of the following congruences have solutions?
x^2 congruent to 8 (mod 53)
x^2 congruent to 15 (mod 31)
x^2 congruent to 54 (mod 7)
x^2 congruent to 625 (mod 9973)
can someone explain how do you tell if a congruence hasno solution? you.
(this comes as a single questions in the book, i am not tryingto ask multiple questions in one post. if this is stillbreaking the rules, i appologize for that).

1. is 4 and 2. is 3

step-by-step explanation:

so if you look at the first one you see that 1 is to 4 and 2 is to 8 and so on, so you can see for every 1 there is a times 4 so if it were 3 then it would be 3*4 and it is 12

for number 2 it is 3 because 1 is to 3 and 2 is to 6 so for every 1 there is 3 so if it were 3 then there would be 3*3 = 9

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step-by-step explanation:

because i said it is

step-by-step explanation :

we know that

the measurement of the outer angle is the semi-difference of the arcs which comprises

in this problem

m< xzy is the outer angle

substitute the values

the measure of angle xoy is equal to

> by central angle

substitute the value