Intro to Elementary Number Theory Homework Problem. The quadratic congruence below has at least one solution modulo 47. Enter the smallest positive integer solution of the quadratic congruence.(Note that 47 is prime.)Type your answer...2x2+3x+5= 0 (mod 47)

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Answered: The quadratic congruence below has at…

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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Part b is the one I need help with
Problem 4. Let n be an integer. Show that if 2 + 2/1+ 12n2 is an integer, then it is the square of an integer.
Problem 4. Let n be any positive integer. Prove that there exists a positive integer k (depending on n) such that the following list of n consecutive integers: k, k + 1, ·, k + n - 1 contains no prime number at all. = Hint. Use the factorial (but k n! is NOT the correct answer, start from this and try to see what are missing). You also need the 2-out-of-3 property of division.
Intro to Elementary Number Theory homework problem.
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6. It is helpful to be able to think about very large numbers in terms of powers of 10. You should be familiar with many of these terms, but have you thought about how many 10's are multiplying each other? Here are some numbers to think about and examples of things that would be counted in these quantities. Fill in the proper power of 10. The first has been done for you. NUMBER POWER OF 10 EXAMPLE The distance between New York City and Boston is approximately 1 million feet. There are approximately 3 billion seconds in a century. There are 6 trillion miles in a light year, i.e. the distance light can travel in a year. There are approximately 1 quadrillion ants populating the earth at any time. There are approximately 8 quintillion grains of sand on all of the Earth's beaches. 1 million = 1,000 -1, 000 = 10 -10° = 10° 1 billion = 1,000 -1 million = 10' -10° = 1 trillion = (1 million) = (10")* = 1 quadrillion =1000-1 trillion = 1 quintillion = (1 billion)' =

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The quadratic congruence below has at least one solution modulo 47. Enter the smallest positive integer solution of the quadratic congruence. (Note that 47 is prime.) Type your answer... 2x2+3x+5=0 (mod 47)