Ta có:
` 6a + 11b `
` = (31a - 25 a) + (186b - 175b) `
` = 31a - 25a + 186b - 175b `
` = 31a - 25a + 31.6b - 25.7b `
` = 31(a + 6b) - 25(a + 7b) `
Vì ` 6a + 11b \vdots 31 <=> 31(a + 6b) - 25(a + 7b) \vdots 31 `
Mà ` 31(a + 6b) \vdots 31 `
` => 25(a + 7b) \vdots 31 `
` => a + 7b \vdots 31 ` ` (đpcm) `