The theory of numbers, by Robert D. Carmichael ...
46 THEORY OF NUMBERS be any linear congruence and let a and m have the greatest common divisor d (d _L ). Then a necessary and sufficient condition for the existence of solutions of the congruence is that c be divisible by d. If this condition is satisfied the congruence has just d solutions, and all the solutions are congruent modulo m/d. EXERCISES i. Find the remainder when 240 is divided by 31; when 243 is divided by 31. 2. Show that 22 +I has the factor 64I. 3. Prove that a number is a multiple of 9 if and only if the sum of its digits is a multiple of 9. 4. Prove that a number is a multiple of ii if and only if the sum of the digits in the odd numbered places diminished by the sum of the digits in the even numbered places is a multiple of ii.
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About this Item
- Title
- The theory of numbers, by Robert D. Carmichael ...
- Author
- Carmichael, Robert Daniel, 1879-
- Canvas
- Page 34
- Publication
- New York,: J. Wiley & sons, inc.; [etc., etc.]
- 1914.
- Subject terms
- Number theory.
Technical Details
- Link to this Item
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https://name.umdl.umich.edu/aam8546.0001.001
- Link to this scan
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https://quod.lib.umich.edu/u/umhistmath/aam8546.0001.001/53
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IIIF
- Manifest
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https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:aam8546.0001.001
Cite this Item
- Full citation
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"The theory of numbers, by Robert D. Carmichael ..." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/aam8546.0001.001. University of Michigan Library Digital Collections. Accessed May 18, 2025.