List the first 3 positive prime numbers d in Z so that the quadratic integers in Q[Vd] are precisely the ones of the form a + byd, where a and b are rational integers. List the first 3 positive prime numbers d so that the quadratic integers in Q[vd] are precisely the ones of the form (a +bVd)/2, where a and b are rational integers and a and b are either both even or both odd. Do the same when vd is replaced by v-d.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 28E: Let and be positive integers. If and is the least common multiple of and , prove that . Note...
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List the first 3 positive prime numbers d in Z so that the quadratic integers in Q[Vd] are
precisely the ones of the form a + byd, where a and b are rational integers. List the first 3
positive prime numbers d so that the quadratic integers in Q[Vd] are precisely the ones of
the form (a + byd)/2, where a and b are rational integers and a and b are either both even
or both odd.
Do the same when vd is replaced by v-d.
Transcribed Image Text:List the first 3 positive prime numbers d in Z so that the quadratic integers in Q[Vd] are precisely the ones of the form a + byd, where a and b are rational integers. List the first 3 positive prime numbers d so that the quadratic integers in Q[Vd] are precisely the ones of the form (a + byd)/2, where a and b are rational integers and a and b are either both even or both odd. Do the same when vd is replaced by v-d.
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