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Let m be an integer. Prove that m and 3m + 2 have the same parity.
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- Let a be an odd integer. Prove that 8|(a21).Let be a nonzero integer and a positive integer. Prove or disprove 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.
- 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=105Let a be an integer. Prove that 3|a(a+1)(a+2). (Hint: Consider three cases.)26. Let be an integer. Prove that . (Hint: Consider two cases.)