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If сх 3D су (тod n) and c >0 then а) х 3Dу (тоd сп) Ь) х%3D у (тod n) с) хну (тod") а) None of thes-

If сх 3D су (тod n) and c >0 then а) х 3Dу (тоd сп) Ь) х%3D у (тod n) с) хну (тod") а) None of thes-

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please what is the answer for this question I put some notes
(a) If a = b (mod n) and m | n, then a = b (mod m). (b) If a = b (mod n) and c > 0, then ca = cb (mod cn). (c) If a = b (mod n) and the integers a, b, n are all divisible by d > 0, then a/d = b/d (mod n/d). Theorem 4.2. Let n > 1 be fixed and a, b,c,d be arbitrary integers. Then the following properties hold: | (a) a = a (mod n). (b) If a = b (mod n), then b = a (mod n). (c) If a = b (mod n) and b = c (mod n), then a = c (mod n). (d) If a = b (mod n) and c= d (mod n), then a + c = b+d (mod n) and ac = bd (mod n). (e) If a = b (mod n), then a +c =b+c (mod n) and ac = bc (mod n). (f) If a = b (mod n), then a* = b* (mod n) for any positive integer k.
Transcribed Image Text:(a) If a = b (mod n) and m | n, then a = b (mod m). (b) If a = b (mod n) and c > 0, then ca = cb (mod cn). (c) If a = b (mod n) and the integers a, b, n are all divisible by d > 0, then a/d = b/d (mod n/d). Theorem 4.2. Let n > 1 be fixed and a, b,c,d be arbitrary integers. Then the following properties hold: | (a) a = a (mod n). (b) If a = b (mod n), then b = a (mod n). (c) If a = b (mod n) and b = c (mod n), then a = c (mod n). (d) If a = b (mod n) and c= d (mod n), then a + c = b+d (mod n) and ac = bd (mod n). (e) If a = b (mod n), then a +c =b+c (mod n) and ac = bc (mod n). (f) If a = b (mod n), then a* = b* (mod n) for any positive integer k.
If cx = cy (mod n) and c > 0 then a) x = y (mod cn) b) x = y (mod n) c) x = y (mod“) d) None of thes
Transcribed Image Text:If cx = cy (mod n) and c > 0 then a) x = y (mod cn) b) x = y (mod n) c) x = y (mod“) d) None of thes
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