Prove or disprove that the fourth power of an odd integer always leaves a remainder of 1 when divided by 16.
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Originally Posted by creativewisdom Prove or disprove that the fourth power of an odd integer always leaves a remainder of 1 when divided by 16. We will prove the proposition: Notice . Then observe that is always even. Thus divides . This means 16 divides .
Originally Posted by Isomorphism We will prove the proposition: Notice . Then observe that is always even. Thus divides . This means 16 divides . Thank you so much for the help. My question, however, is how did you derive this proposition?
Originally Posted by creativewisdom Thank you so much for the help. My question, however, is how did you derive this proposition? Well... thats what my previous post did...I derived the result. Were you not looking for a proof?
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