13a 02, 208, 498 a perfect square?Justify your conclusion,12. (a) Use the result in Proposition 3.33 to help prove that for each integer a,if 5 divides a?, then 5 divides a.(b) Prove that the real number 5 is an irrational number.13. (a) Prove that for each integer a, if a 0 (mod 7), then a2 # 0 (mod 7).(b) Prove that for each integer a, if 7 divides a, then 7 divides a.(c) Prove that the real number 7 is an irrational number.(a) If an integer has a remainder of 6 when it is divided by 7, is it possible todetermine the remainder of the square of that integer when it is dividedby 7? If so, determine the remainder and prove that your answer is14.correct.(b) If an integer has a remainder of 11 when it is divided by 12, is it pos-sible to determine the remainder of the square of that integer when itis divided by 12? If so, determine the remainder and prove that youranswer is correct.(c) Let n be a natural number greater than 2. If an integer has a remainderof n-1 when it is divided by n, is it possible to determine the remainderof the sauare of that integer whit is divided buL n? If.

Name: 13a 02, 208, 498 a perfect square?Justify your conclusion,12. (a) Use
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Description: 13a 02, 208, 498 a perfect square?Justify your conclusion,12. (a) Use the result in Proposition 3.33 to help prove that for each integer a,if 5 divides a?, then 5 divides a.(b) Prove that the real number 5 is an irrational number.13. (a) Prove that f