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A necessary (but not sufficient) condition for solvability is that n is not divisible by 4 or by a prime of form 4k + 3. [note 3] Thus, for example, x 2 − 3 y 2 = −1 is never solvable, but x 2 − 5 y 2 = −1 may be. [27] The first few numbers n for which x 2 − n y 2 = −1 is solvable are with only one trivial solution: 1
Simplification is the process of replacing a mathematical expression by an equivalent one that is simpler (usually shorter), according to a well-founded ordering. Examples include:
Each of the fourteen congruent heptagonal triangles has one green side, one blue side, and one red side.. In Euclidean geometry, a heptagonal triangle is an obtuse, scalene triangle whose vertices coincide with the first, second, and fourth vertices of a regular heptagon (from an arbitrary starting vertex).
For instance, to solve the inequality 4x < 2x + 1 ≤ 3x + 2, it is not possible to isolate x in any one part of the inequality through addition or subtraction. Instead, the inequalities must be solved independently, yielding x < 1 / 2 and x ≥ −1 respectively, which can be combined into the final solution −1 ≤ x < 1 / 2 .
The silver ratio is a Pisot number, [5] the next quadratic Pisot number after the golden ratio. By definition of these numbers, the absolute value 2 − 1 {\displaystyle {\sqrt {2}}-1} of the algebraic conjugate is smaller than 1, thus powers of σ {\displaystyle \sigma } generate almost integers and the sequence σ n mod 1 ...
10, 9, 8, 7, 6, 5, 4, 3, 2, 1 is the fourth studio album by Midnight Oil, released in 1982 by Columbia Records. It hit number 3 on the Australian Kent Music Report Albums Chart during 171 total weeks. [1] The band's first US release, it peaked at number 178 on the Billboard 200. At the Countdown Music Awards, it was nominated for Best ...
15560 Ensembl n/a ENSMUSG00000041380 UniProt P28335 P34968 RefSeq (mRNA) NM_001256761 NM_000868 NM_001256760 NM_008312 RefSeq (protein) NP_000859 NP_001243689 NP_001243690 NP_032338 Location (UCSC) n/a Chr X: 145.75 – 145.98 Mb PubMed search Wikidata View/Edit Human View/Edit Mouse The 5-HT 2C receptor is a subtype of the 5-HT2 receptor that binds the endogenous neurotransmitter serotonin (5 ...
Sveriges riksdags health ministry Statens folkhälsoinstitut classified 2C-T-4 as "health hazard" under the act Lagen om förbud mot vissa hälsofarliga varor (translated Act on the Prohibition of Certain Goods Dangerous to Health) as of Jul 15, 2007, in their regulation SFS 2007:600 listed as 2,5-dimetoxi-4-isopropyltiofenetylamin (2C-T-4), making it illegal to sell or possess.