Question

if a divides b and a divides c then a divides bx+cy

Answer 1

2 Let a and b be integers such that a divides b+2 and a divides c-1. Let a, b and c be integers such that a divides b and a divides c. Then there exist integers m and n such that b = am and c = an, so bx + cy = (am)x + (an)y = a(mx + ny) and mx + ny is an integer, so a divides bx + cy.

Answer 2

a divides bx + cy.

Given,

a divides b and a divides c

To find,

Prove that a divides bx+cy

Solution,

Let a and b be integers such that a divides b+2 and a divides c-1.

Let a, b and c be integers such that a divides b and a divides c.

Then there exist integers m and n such that b = am and c = an

so,

bx + cy = (am)x + (an)y

             = a(mx + ny)

and,

mx + ny is an integer

∴a divides bx + cy.

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