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6. Use the Euclidean algorithm to find gcd(54321, 50).

6. Use the Euclidean algorithm to find gcd(54321, 50).

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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Number 6
ures (MTH): -29/materials/gp/5853413186 ework - Googl.. /1 > 国 ab 154% fiction books to take with you on your vacation? (b) For the driving part of your vacation you will take 6 of the 35 rock CDs collection, 3 of the 22 classical CDs, and 1 of the 8 comedy CDs. In how ways can you make your choice(s)? 5. Show that for positive integers n, k withn>k, P(n, k) = P(n - 1, k) + k P(n - 1, k – 1). 6. Use the Euclidean algorithm to find gcd(54321, 50). 7. Find the remainder of 61155 when divided by the following. (a) 3 (b) 5 8. Suppose a, b, c, m, n E Z. Prove that if a|b and a c, then a (mb+ nc). 9. Suppose r E Z. Prove that if x 1 (mod 5), then x 1 (mod 5). 10. Let a, b eZ and n e N. Prove that if a = b (mod n), then ged(a, n) ged(b, n). 点 prt sc home end
Transcribed Image Text:ures (MTH): -29/materials/gp/5853413186 ework - Googl.. /1 > 国 ab 154% fiction books to take with you on your vacation? (b) For the driving part of your vacation you will take 6 of the 35 rock CDs collection, 3 of the 22 classical CDs, and 1 of the 8 comedy CDs. In how ways can you make your choice(s)? 5. Show that for positive integers n, k withn>k, P(n, k) = P(n - 1, k) + k P(n - 1, k – 1). 6. Use the Euclidean algorithm to find gcd(54321, 50). 7. Find the remainder of 61155 when divided by the following. (a) 3 (b) 5 8. Suppose a, b, c, m, n E Z. Prove that if a|b and a c, then a (mb+ nc). 9. Suppose r E Z. Prove that if x 1 (mod 5), then x 1 (mod 5). 10. Let a, b eZ and n e N. Prove that if a = b (mod n), then ged(a, n) ged(b, n). 点 prt sc home end
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