A number theory problem by أحمد الحلاق
Number Theory
Level
3
What is the number of perfect squares whose last two digits are 99?
Infinity
0
3
2
1
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1 solution
С^2=100q+99 (q is an integer). C^2 is an odd number, in this case c^2 (mod 4)≡1. However, (100q+99) (mod 4)≡3. Therefore, the equation has no integer solutions. In other words, number of perfect squares is 0 .