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№ 31 (160), 2020 . Ё
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SPLITTING ODD NUMBERS INTO SUMMANDS WITH THE PARTICIPATION OF PRIME NUMBERS Evgeniy Amosov associate professor, Samara state technical university Russia, Samara
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ABSTRACT It is shown that any odd number starting from 3 can be represented as the sum of a prime number and a multiple of 6. : , Keywords: prime numbers, decomposition into term. ё 6n±1 [1,2].
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N=(6k–1) + (6m–1) + (6l–1) =(6(k–1)+6–1) + (6m– 1) + (6l–1), N=(6(k–1)+6m+6l) + 3,
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N=((6k+1) + (6m–1)) + (6l±1).
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3=6∙0+3, 5=6∙0+5, 7=6∙0+7, 9=6∙1+3, 11=6∙1+5, 13=6∙1+7, 15=6∙2+3, 17=6∙2+5. ,
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6l±1–6z <25,
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N N=(6k±1) + (6m±1) + (6l±1), .
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N= (6k +6m+6z) + (6l±1–6z), ,
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N=(6k+6m+6l) + 3. ,
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6k+6.
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