Life with and without the fundamental theorem. (4 marks) (a) prove (without using the fundamental theorem of arithmetic) that if gcd(a, b) = 1 and ac and b c, then ab c. (b) now give a shorter (better? ) proof of this fact which appeals to the fundamental theorem of arithmetic. (hint: interpret the hypothesis and conclusion in terms of prime factorizations.)

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Select the correct answer. sean is a computer programmer. he has programmed an application for toddlers that plays nursery rhymes. however, a logic error has occurred in the program. which problem is a likely consequence of the error? a. the program crashes every time the user wants to play the nursery rhymes. b. the program crosses its buffer boundaries and overwrites an adjacent program. c. the program plays a different nursery rhyme than the one the user intended to play. d. the program shows different structures in its programming language code. e. the program introduces new viruses every time the user plays a nursery rhyme.