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(ii) The first few cubes are 1,8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, and 1728. Write 1729 as a sum of two cubes in two different ways and hence factorise 1729 as a product of primes. Show that if p is a prime factor of 1729, and a is a number with (a, p) = 1, then a 1728 = 1 mod p, and hence if (a, 1729) = 1, then 1728 = 1 mod 1720

(ii) The first few cubes are 1,8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, and 1728. Write 1729 as a sum of two cubes in two different ways and hence factorise 1729 as a product of primes. Show that if p is a prime factor of 1729, and a is a number with (a, p) = 1, then a 1728 = 1 mod p, and hence if (a, 1729) = 1, then 1728 = 1 mod 1720

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(ii) The first few cubes are 1,8, 27,64, 125, 216, 343, 512, 729, 1000, 1331, and 1728. Write 1729 as a sum of two cubes in two different ways and hence factorise 1729 as a product of primes. Show that if p is a prime factor of 1729, and a is a number with (a, p) = 1, then al728 = 1 mod p, and hence if (a, 1729) = 1, then = 1 mod 1729. р, 1728 а
Transcribed Image Text:(ii) The first few cubes are 1,8, 27,64, 125, 216, 343, 512, 729, 1000, 1331, and 1728. Write 1729 as a sum of two cubes in two different ways and hence factorise 1729 as a product of primes. Show that if p is a prime factor of 1729, and a is a number with (a, p) = 1, then al728 = 1 mod p, and hence if (a, 1729) = 1, then = 1 mod 1729. р, 1728 а
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