[理工] [離散] 數論

[Lautreamont (Maldoror is dead)]

which of the next following linear equation has solution in integers?
Please show the reason.
(a) 28x + 16y = 6
(b) 51x + 18y = 12
(c) 21x + 35y = 45

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推 gsrr:X,Y係數取最大公因數,如果能造出等號右邊的數字就有整數解
推 luckysky1:同樓上
→ Lautreamont:所以是在x,y系數化簡成互值的情況下，等號右邊是整數?
推 luckysky1:恩
→ EntHeEnd:答案是不是a b 都可以 c不行  ?
→ EntHeEnd:a也不行才對
推 assassin88:答案是b吧= =
→ EntHeEnd:恩 我也算b
→ Lautreamont:b