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Question: need help with 332 amp 333 and its graph theory...

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Need help with 3.3.2 & 3.3.3 and its graph theory

History of math textboc XV O o file//c/Users/MiD9s/Desktop/Histo EXERCISES We can now fill the gap in the proof of Euclids theorem on perfect numbers (previous exercise set), using the prime divisor property 3.3.1 Use the prime divisor property to show that the proper divisors of 2-p, for any odd prime p, are 1,2,22... . 2- 1 and p. 2p, 22p2 2p. The result that if gada, b)-1 then I = ma + nb for some integers m and n is a special case of the following way to represent the ged. 3.3.2 Show that, for any integers a and b, there are integers m and n such that gcd(a, b)-ma + nb. This in turn gives a general wa to find integer solutions of lincar equations. c with integer 33.3 Deduce from Exercise 3.3.2 that the equation ax + by cocfficients a, b, and c has an integer solution x, y if ged(a, b) divides c. The converse of this result is also valid, as one discovers when considering a necessary condition for ax + by c to have an integer solution. 3.3.4 The equation 12x+ 15y I has no integer solution. Why? 33.5 (Solution of lincar Diophantine equations) Give a lest to decide, for any given integers a, b, c, whether there are integers x, y such that ax + by c.
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