172 (number)
172 (one hundred ndseventy-two) is the natural number following 171 and preceding 173. In mathematics 172 is a part of a near-miss for being a counterexample to 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 , , and satisfy the equation for any integer value of greater than 2. The cases and have been k ..., as 1353 + 1383 = 1723 − 1. This is only the third near-miss of this form, two cubes adding to one less than a third cube. It is also a "thickened cube number", half an odd cube (73 = 343) rounded up to the next integer. See also * 172 (other) References {{DEFAULTSORT:172 (Number) Integers ...
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Natural Number
In mathematics, the natural numbers are those numbers used for counting (as in "there are ''six'' coins on the table") and ordering (as in "this is the ''third'' largest city in the country"). Numbers used for counting are called ''Cardinal number, cardinal numbers'', and numbers used for ordering are called ''Ordinal number, ordinal numbers''. Natural numbers are sometimes used as labels, known as ''nominal numbers'', having none of the properties of numbers in a mathematical sense (e.g. sports Number (sports), jersey numbers). Some definitions, including the standard ISO/IEC 80000, ISO 80000-2, begin the natural numbers with , corresponding to the non-negative integers , whereas others start with , corresponding to the positive integers Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). The natural ...
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171 (number)
171 (one hundred ndseventy-one) is the natural number following 170 and preceding 172. In mathematics 171 is a triangular number and a Jacobsthal number. There are 171 transitive relations on three labeled elements, and 171 combinatorially distinct ways of subdividing a cuboid by flat cuts into a mesh of tetrahedra, without adding extra vertices. The diagonals of a regular decagon meet at 171 points, including both crossings and the vertices of the decagon. There are 171 faces and edges in the 57-cell, an abstract 4-polytope with hemi-dodecahedral cells that is its own dual polytope. See also * The year AD 171 Year 171 (Roman numerals, CLXXI) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Severus and Herennianus (or, less frequently, year 92 ... or 171 BC * List of highways numbered 171 * References {{DEFAULTSORT:171 (Number) Integers ...
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173 (number)
173 (one hundred ndseventy-three) is the natural number following 172 and preceding 174. In mathematics 173 is: *an odd number. *a deficient number. *an odious number. *a balanced prime. *an Eisenstein prime with no imaginary part. *a Sophie Germain prime. *an inconsummate number. *the sum of 2 squares: 22 + 132. *the sum of three consecutive prime numbers: 53 + 59 + 61. * Palindromic number in bases 3 (201023) and 9 (2129). In astronomy * 173 Ino is a large dark main belt asteroid * 173P/Mueller is a periodic comet in the Solar System * Arp 173 (VV 296, KPG 439) is a pair of galaxies in the constellation Boötes In the military * 173rd Air Refueling Squadron unit of the Nebraska Air National Guard * 173rd Airborne Brigade Combat Team of the United States Army based in Vicenza * 173rd Battalion unit of the Canadian Expeditionary Force during the World War I * 173rd Surveillance Squadron (Australia) of the Australian Army at Oakey, Queensland * K-173 ''Chelya ...
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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 , , and satisfy the equation for any integer value of greater than 2. The cases and have been known since antiquity to have infinitely many solutions.Singh, pp. 18–20. The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of '' Arithmetica''. Fermat added that he had a proof that was too large to fit in the margin. Although other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to doubt that Fermat ever had a correct proof. Consequently the proposition became known as a conjecture rather than a theorem. After 358 years of effort by mathematicians, the first successful proof was released in 1994 by Andrew Wiles and form ...
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172 (other)
172 may refer to: * The year 172 of the Gregorian calendar * The number 172 (number) * The Cessna 172 "Skyhawk", a single engine, high wing, light airplane produced by Cessna Aircraft Company * 172 BC * British Rail Class 172 The British Rail Class 172 is a British diesel multiple unit (DMU) passenger train built by Bombardier Transportation's Derby Litchurch Lane Works for use on inner-suburban passenger services. The class is currently operated by West Midlands Ra ...