Guys, this is a very interesting question , I have seen this type for the first time. I have couple of questions
1) if remainder for t/7 is known we can know the remainder for t^2/7 , and vice verca is not possible ?
ie if the the remainder for t^2/7 is known t/7 is not known ?
2) where can I get additional information on these types of questions ?
Actually there is a remainder rule, that works only for additions, subtractions and multiplications, but not for divisions.
Ill illustrate this rule with an example.
25/7 - R= 4
41/7 - R= 6addition
(25+41)/7 should give remainder of 4+6, but 10 is greater than 7, so the final remainder will be that of 10/7, ie 3
checking this rule - 25+41 = 66..... 66/7 - R = 3subtraction
(41-25)/7 should give remainder 6-4 = 2...... check: 41-25 = 16. .....16/7 - R= 2multiplication
41*25/7 should give remainder of (6*4)/7, ie 24/7 -> R= 3
check: 41*25 = 1025....1025/7 -> R= 3
Now square is nothing but (t/7) * (t/7), so applying multiplication rule, we get that remainder should be R*R
Square root is division, and therefore the rule doesnt apply to square roots.
Hope this helps