Number Theory Number Theory: A reflection of the basic mathematical endeavor. Exploration Of Patterns: Number theory abounds with patterns and requires little background to understand questions. Inductive Reasoning: Patterns are discovered and generalized.
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Number Theory: A reflection of the basic mathematical endeavor.
Exploration Of Patterns: Number theory abounds with patterns and requires little background to understand questions.
Born: about 569 BC in Samos, IoniaDied: about 475 BC
-Basis of philosophy and religion
-Imparted to them humanistic and mystic properties.
33, 550, 336
8, 589, 869, 056
137, 438, 691, 328
2, 305, 483, 008, 139, 952, 128
Born: 7 Dec 1823 in Liegnitz, Prussia (now Legnica, Poland)Died: 29 Dec 1891 in Berlin, Germany
Born: 30 April 1777 in Brunswick, Duchy of Brunswick (now Germany)Died: 23 Feb 1855 in Göttingen, Hanover (now Germany)
Born: 15 April 1707 in Basel, SwitzerlandDied: 18 Sept 1783 in St Petersburg, Russia
Born: 17 Aug 1601 in Beaumont-de- Lomagne, FranceDied: 12 Jan 1665 in Castres, France
There are no non-zero whole numbers a, b, c where a n + b n = c nfor n a whole number greater than 2.
a 2 + b 2 = c 2
b is a multiple of a
a is a divisor of b
a | b a does not divide b
Let S(n) be a statement involving the integers n. Suppose for some fixed integer no two properties hold:
a Real, a 0.
Proof: Basis Step: a o = 1 so true for n = 0
Induction Step: Suppose for some integer k
that a k = 1 then
ak+1 = a k a k / ak-1 = (1 1)/1 = 1
By induction an = 1.
then 4 | n.
Since 7 | 77, then 7 | 515,592