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Fermat’s Last Theorem No positive integers a, b, c satisfy the equation:

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1 LO Batory September 5, 2017

THEOREMS & CONJECTURES

Fermat’s Last Theorem No positive integers a, b, c satisfy the equation:

a

n

+ b

n

= c

n

for any integer n greater than 2.

Goldbach’s Conjecture Every even integer greater than 2 can be expressed as a sum of two primes.

Pythagorean Theorem In a right triangle the square of the hypotenuse is equal to the sum of the squares of the remaining sides.

CONDITIONAL STATEMENTS

1. Let x ∈ Z. Prove that if 7x + 9 is even, then x is odd.

2. Let x ∈ Z. Prove that if x

2

− 6x + 5 is even, then x is odd.

3. Let x, y ∈ R. Prove that if y

3

+ yx

2

¬ x

3

+ xy

2

then y ¬ x.

Cytaty

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