where can I find phase diagram for Fe-Mn-C ?
Does anyone know a way to find integers a,b such that
Elijah Wood
Bentley Parker
Let B be an odd integer.
Then (B-1) and (B+1) are even, and so
(B-1)*(B+1) is even. Assume
we can find an odd integer A
that divides (B-1)*(B+1). Set
a = (A+B)/2, b=(A-B)/2 and
k = A-((B-1)*(B+1))/A.
Then a+b = A while
4*a*b+1 = 4*(A+B)/2*(A-B)/2 + 1 =
A^2-B^2+1=A^2-(B-1)*(B+1)
= A* ( A- (B-1)*(B+1)/A )
= (a+b)*k
which is dividble by (a+b).
Example: Take B=13. Then (B-1)*(B+1)=168
=8*21, and we can take A=21. Then
a=(A+B)/2=17, b=(A-B)/2=4,
k=21-8=13. Check:
(4*17*4+1)/(17+4)=13.
Isaiah Jenkins
Note (B-1)*(B+1) will be divisible by an odd number A>1 unless (B-1)*(B+1) is a power of 2, i.e. unless (B-1) and (B+1) are powers of 2, i.e. unless B=3. If B=3, can take A=1.