Number Theory

LECTURE 7: Number Theory

Areas in number theory (NT): Combinatorial, algebraic, analytical, transcendental, geometric, and computational NT.
Number Theory Conjectures and Theorems

Conjecture 1 (pyramidal conj): Any integer can be expressed in the sum of no more than five such pyramidal numbers.
Theorem 2 (4-square thm): Equation is solvable for all n with integer solutions.
Conjecture 3 (Catalan's conj): Are 8 and 9 the only consecutive powers? . In other words, can you find integer solutions for besides the above?
Theorem 4 (Fermat's last thm): has no non-zero integer solutions for z, y, and z when n>2.
Conjecture 5 (Goldbach Conj): Any even number larger than 2 is the sum of two prime numbers.

Last Modified: 10/10/00