Combinatorics-Kenneth Rosen (Ex 5.2 12)

Question

How many ordered pairs of integers (a,b) are needed to guarantee that there are two ordered pairs ($a_{1}$,$b_1$) and

($a_2,b_2)$ such that $a_1$ mod 5=$a_2$ mod 5 and $b_1$ mod 5=$b_2$ mod 5?

My answer comes to be 26. Please confirm.

Comments

Yes answer will be 26 because a can have 5(0,1,2,3,4) values and b can have 5 values and 5*5 = 25 ordered pairs are possible with each distinct pair of class now by the rule of pigeonhole if we add 1 then there exist at least two pair which belong to the same class.

so total no of ordered pairs = 25 +1 =26

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https://gateoverflow.in/219084/number-of-ordered-pairs

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Yes. Answer is 26. Refer the link srestha ma'am shared if any doubt.