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If two primes which end in 3 or 7 and surpass by 3 a multiple of 4 are multiplied, then their product will be composed of a square and the quintuple of another square. In other words, if p, q are of the form 20k + 3 or 20k + 7, then pq = x 2 + 5y 2. Euler later extended this to the conjecture that
Microsoft Math 2.0: Part of Microsoft Student 2007 Microsoft Math 3.0 : Standalone commercial product that requires product activation ; includes calculus support, digital ink recognition features and a special display mode for video projectors
See calendar and list of calendars for other groupings of years. See history , history by period , and periodization for different organizations of historical events. For earlier time periods, see Timeline of the Big Bang , Geologic time scale , Timeline of evolution , and Logarithmic timeline.
1000 yr: Also called "kiloannum". Age: 2 148 and 2/3 of a year: A superstitious unit of time used in astrology, each of them representing a star sign. terasecond: 10 12 s: About 31,709 years. megaannum: 10 6 yr: Also called "megayear". 1000 millennia (plural of millennium), or 1 million years (in geology, abbreviated as Ma). petasecond: 10 15 s ...
This corresponds to a set of y values whose product is a square number, i.e. one whose factorization has only even exponents. The products of x and y values together form a congruence of squares. This is a classic system of linear equations problem, and can be efficiently solved using Gaussian elimination as soon as the number of rows exceeds ...
In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit Hindu-Arabic numerals (positional notation) that is simple enough to perform by hand.
For example, log 2 (8) = 3, because 2 3 = 8. The graph gets arbitrarily close to the y axis, but does not meet or intersect it . An exponential equation is one which has the form a x = b {\displaystyle a^{x}=b} for a > 0 {\displaystyle a>0} , [ 43 ] which has solution
The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial (x + 1) 2 = x 2 ...