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Let a, b, c 2 Z+.
(a) Prove that if a|b, then ac|bc for all c.
(b) If a|bc, can you conclude that either a|b or a|c? Justify your answer with a proof or a counter example.
(c) Prove that gcd(a, a + b) = gcd(a, b).
Q. Find the number of ways three letter "words" can be chosen from the alphabet if none of the letters can be repeated? Solution: There are 26 ways of choosing the first lett
The ratio between the length and breadth of a rectangular field is 11:7. The cost of fencing it is Rs. 75,000. Find the dimensions of the field
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George worked from 7:00 A.M. to 3:30 P.M. with a 45-minute break. If George earns $10.50 per hour and does not obtain paid for his breaks, how much will he earn? (Round to the near
The Robin's Nest Nursing Home had a fundraising target of $9,500. By the end of the fundraiser, they had exceeded their goal through $2,100. How much did they raise? Exceeded
Susan begins work at 4:00 and Dee starts at 5:00. They both finish at the similar time. If Susan works x hours, how many hours does Dee work? Since Susan started 1 hour before
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