If a statement is true prove it If a statement is false disp

If a statement is true, prove it. If a statement is false, disprove it. : There exist integers a and b for which 42a + 7b = 1.

Solution

Statement is false.

Let , there exist a and b so that:

42a+7b=1

7 |42 and 7|7 hence, 7|(42a+7b)

But 7 does not divide 1

Hence, a contradiction

Hence, there do not exist a,b so that:42a+7b=1