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... Theorem. Every sufficiently large even integer n > 46 can be expressed as the sum of abundant numbers a and b thus: a + b = n. Proof. First we rewrite n = 2x (where x is some positive integer) as n = 20m+r, where r satisfies n ≡ r mod 20 and m = n−r 20 . If r = 0, then we’re done, we can simply set ...
... Theorem. Every sufficiently large even integer n > 46 can be expressed as the sum of abundant numbers a and b thus: a + b = n. Proof. First we rewrite n = 2x (where x is some positive integer) as n = 20m+r, where r satisfies n ≡ r mod 20 and m = n−r 20 . If r = 0, then we’re done, we can simply set ...
Complex Numbers
... if you add together two real numbers, you get a real number as always: 2+3=6; if you add two imaginary numbers, you get an imaginary number: 2+3 = 6; BUT if you add an imaginary number to a real number, what do you get? 2+3 can be neither real nor imaginary, it must be a combination of the two. ...
... if you add together two real numbers, you get a real number as always: 2+3=6; if you add two imaginary numbers, you get an imaginary number: 2+3 = 6; BUT if you add an imaginary number to a real number, what do you get? 2+3 can be neither real nor imaginary, it must be a combination of the two. ...
Mathematics of radio engineering
The mathematics of radio engineering is the mathematical description by complex analysis of the electromagnetic theory applied to radio. Waves have been studied since ancient times and many different techniques have developed of which the most useful idea is the superposition principle which apply to radio waves. The Huygen's principle, which says that each wavefront creates an infinite number of new wavefronts that can be added, is the base for this analysis.