Bachet`s Equation - Math-Boise State
... We looked at integers < p where p is prime. We also looked at an identity element for each group. Our spreadsheet was organized into 4 major columns: Zp , k , |S|, and |S| ∪ IDg Where Zp is the range to which we confine our search k is the specific constant we are looking at |S| is the solution size ...
... We looked at integers < p where p is prime. We also looked at an identity element for each group. Our spreadsheet was organized into 4 major columns: Zp , k , |S|, and |S| ∪ IDg Where Zp is the range to which we confine our search k is the specific constant we are looking at |S| is the solution size ...
Discovering Exactly when a Rational is a Best
... This theorem is stated in the terms of Mobius himself, however, we will analyze the theorem a little and rephrase it for our purposes without affecting the validity of the theorem. First, note that since ϕ is irrational, ϕ times an integer and then plus or minus a rational number is certainly still ...
... This theorem is stated in the terms of Mobius himself, however, we will analyze the theorem a little and rephrase it for our purposes without affecting the validity of the theorem. First, note that since ϕ is irrational, ϕ times an integer and then plus or minus a rational number is certainly still ...
Proofs by induction - Australian Mathematical Sciences Institute
... • On every even-numbered move, shift one of the other discs (not the smallest). There will only ever be one possible move to make. Can you give a proof by induction that this works? ...
... • On every even-numbered move, shift one of the other discs (not the smallest). There will only ever be one possible move to make. Can you give a proof by induction that this works? ...
the linear difference-differential equation with linear coefficients
... and this function is integrable up to the origin along a path on which0. We suppose the f-plane to be cut along the line arg f =ir and
take z to be a point on the circle | f | = | s\ in this cut plane, with %(Arz~l) >0.
We denote by Q(z, s) the arc of this circle joining the points 2 and ...
... and this function is integrable up to the origin along a path on which
THE DEVELOPMENT OF THE PRINCIPAL GENUS
... on to observe that the conjecture is only true in general when a and b are allowed to be rational numbers, and gives the example 89 = 4 · 22 + 1, which can be written as 89 = 11( 25 )2 + ( 92 )2 but not in the form 11a2 + b2 with integers a, b. Thus, he says, the theorem has to be formulated like th ...
... on to observe that the conjecture is only true in general when a and b are allowed to be rational numbers, and gives the example 89 = 4 · 22 + 1, which can be written as 89 = 11( 25 )2 + ( 92 )2 but not in the form 11a2 + b2 with integers a, b. Thus, he says, the theorem has to be formulated like th ...
Bounded negativity of Shimura curves
... be of type 2 A2,r , where d|3, d ≥ 1, 2rd ≤ 3. In other words, GF0 = SU (h) where h is a hermitian form constructed as follows. Start with a totally real field F0 and take a totally complex quadratic extension F/F0 , i.e. F is a CM field. Then take a central simple division algebra D of degree d (he ...
... be of type 2 A2,r , where d|3, d ≥ 1, 2rd ≤ 3. In other words, GF0 = SU (h) where h is a hermitian form constructed as follows. Start with a totally real field F0 and take a totally complex quadratic extension F/F0 , i.e. F is a CM field. Then take a central simple division algebra D of degree d (he ...
Fermat's Last Theorem
In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two. The cases n = 1 and n = 2 were known to have infinitely many solutions. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica where he claimed he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The theretofore unsolved problem stimulated the development of algebraic number theory in the 19th century and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics and prior to its proof it was in the Guinness Book of World Records for ""most difficult mathematical problems"".