Hi, I've asked the question below last week and have received fantastic results, but I just don't understand them.
Prove that 43 ^ n + 83 x 92 ^ 3n – 1 is divisible by 7 for all positive integers n,
Can you please help by either:
Defining the following two answers into simpler terms, enough for a young teenager to understand:
Reduce mod 7: 43^n= 1^n=1mod7
83=6mod7 and 92^(3n-1) =(13*7+1)^(3n-1)=1^(3n-1)=1mod...
Plug these in : 1 + 6(1) =7mod 7. Therefore your expression
is divisible by 7 for all n.
or
43 to any power mod 7 always =1
92 to any power mod 7 always =1
83 mod 7 =6
so 1+1*6 is the mod of the whole expression for any n. Which is divisible by 7.
OR
Answer the question with a new answer, making it as simple as possible. Thanks.
2007-07-12
01:14:07
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3 answers
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asked by
Elder Price
2