Please prove the following statement, in FULL detail. (by the if
and only if proving technique,...
Please prove the following statement, in FULL detail. (by the if
and only if proving technique, not induction!)
Prove that 5 | Un if and only if 5|n. Where Un is the Fibonacci
sequence.
Number Theory Course , I need a full explained answer for those
proofs please
1. Prove...
Number Theory Course , I need a full explained answer for those
proofs please
1. Prove that for every integer x, x + 4 is odd if and only if x
+ 7 is even.
2. Prove that for every integer x, if x is odd then there exists an
integer y such that x^2 = 8y + 1.
Fibonacci Numbers.
The Fibonacci numbers are
1,1,2,3,5,8,13,21,….1,1,2,3,5,8,13,21,….
We can define them inductively by f1=1,f1=1, f2=1,f2=1, and...
Fibonacci Numbers.
The Fibonacci numbers are
1,1,2,3,5,8,13,21,….1,1,2,3,5,8,13,21,….
We can define them inductively by f1=1,f1=1, f2=1,f2=1, and
fn+2=fn+1+fnfn+2=fn+1+fn for n∈N.
Prove that fn=[(1+√5)n−(1−√5)n]/2n√5.