Answer to Question #72049 in Discrete Mathematics for Chen Qing Kang

Question

Prove the following statement by contradiction.
“There is no integer solution to the equation
(x^2)-6=0 ."

Prove and disprove the following statements.
(a) For all the odd integers n, n^4 mod 8 = 1
(b) There exist positive integers a, b and ab, which all the three belong to perfect
squares.”

State the contrapositive for the statement given below and hence, provide a proof for the
statement.
“For all integers a and b, if ab is even, then at least one of a or b is even.”

Prove or disprove the following statement.
“Let p and q be positive integers, if p mod 4 = 1 and q mod 4 = 2, then pq mod 4 = 2.”

Answer 1

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