Division & Divisibility. Division. a divides b if a is not zero there is a m such that a.m = b “a is a factor of b” “b is a multiple of a” a|b. Division. If a|b and a|c then a|(b+c) “ If a divides b and a divides c then a divides b plus c ”. a|b a.x = b a|c a.y = c
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Theorem 1 (page 202, 6th ed, page 154, 5th ed)
a divided by d = q remainder r
NOTE: remainder r is positive and divisor d is positive
Troubled by this?
Did you expect q = -3 and r = -2?
What if 3 of you went to a café and got a bill for £11?
Would you each put £3 down and then leg it?
Or £4 each and leave £1 tip?