cannot understand junior problem solution

[egal]

what is the significance of mod 3 and mod 8 that we used them in this solution and I don't understand how they got this expression:

thanks in advance

 

[blamocur]

There are 5 squares of which $5-a$ are divisible by 3 and $a$ of them have remainder 1 when divided by one. $1\cdot a$ is the same as just $a$. From that we know that $a$ has remainder of 1 when divided by 3, and since $0 \leq a \leq 5$ we know that $a$ can be either 1 or 4.
Does this make sense?

 

[egal]

There are 5 squares of which $5-a$ are divisible by 3 and $a$ of them have remainder 1 when divided by one. $1\cdot a$ is the same as just $a$. From that we know that $a$ has remainder of 1 when divided by 3, and since $0 \leq a \leq 5$ we know that $a$ can be either 1 or 4.
Does this make sense?

yes, you get the remainder 1 from a of them and 0 from (5-a) of them since 3|(5-a) of them, I got this part

 

[blamocur]

There are 5 squares of which $5-a$ are divisible by 3 and $a$ of them have remainder 1 when divided by one. $1\cdot a$ is the same as just $a$. From that we know that $a$ has remainder of 1 when divided by 3, and since $0 \leq a \leq 5$ we know that $a$ can be either 1 or 4.
Does this make sense?

Correction: since we are talking about primes "divisible by 3" means "equal to 3" of course.

 

[blamocur]

yes, you get the remainder 1 from a of them and 0 from (5-a) of them since 3|(5-a) of them, I got this part

Does the rest make sense too?
To answer your question about the significance of 3 and 8: there is none, i.e., whatever works

 

[egal]

Does the rest make sense too?
To answer your question about the significance of 3 and 8: there is none, i.e., whatever works

yeah I got it not, thanks for your help