Let a, b e R. Prove that if 15a + 206 = 49, then a and b are not both integers.

20. If and are nonzero integers and is the least common multiple of and prove that.

Let and be positive integers. If and is the least common multiple of and , prove that . Note that it follows that the least common multiple of two positive relatively prime integers is their product.

Let ,, and be integers. Prove or disprove that implies or .

Prove that if and are integers such that and , then either or .

Find the greatest common divisor of a,b, and c and write it in the form ax+by+cz for integers x,y, and z. a=14,b=28,c=35 a=26,b=52,c=60 a=143,b=385,c=65 a=60,b=84,c=105

Let , and be integers . Prove or disprove that implies.

15. Assume that are in and with and invertible. Solve for.

Let a,b,c and d be integers such that ab and cd. Prove that acbd.