The IMO performs once a year, and has become an important activity in the field of mathematics. Because the problems in IMO are very difficult, and in general needs two days to finish the test of only six problems, therefore, it is significant to study how to solve and solve those IMO problems with various methods. With respect to question (a) of the problem of discussing, at first, using the so-called “exhaustive method” and the mathematical induction, the paper gets the conclusion of that if n is the integral multiple of 3, subtracting 1 from the nth power of 2 must be divisible by 7. Furthermore, it also proves by use of the disprove method that if n is not the integral multiple of 3, subtracting 1 from the nth power of 2 is impossible to be divisible by 7. The way of solving question (b) is similar to that of solving (a), in order to use the result of question (a) for the third step of the mathematical induction, the paper firstly consider the third power of that 1 added to (k+1)th power of 2 and applying the disprove method proves that it and hence that 1 added to the (k+1)th power of 2 are not divisible by 7, namely the question (b) is true.
Published in | International Journal of Systems Science and Applied Mathematics (Volume 5, Issue 1) |
DOI | 10.11648/j.ijssam.20200501.11 |
Page(s) | 1-3 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2020. Published by Science Publishing Group |
IMO, The Mathematical Induction, Algebraic Equation, Disprove Method
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APA Style
Zhang Yue. (2020). A Different Method of Solving a Problem of IMO. International Journal of Systems Science and Applied Mathematics, 5(1), 1-3. https://doi.org/10.11648/j.ijssam.20200501.11
ACS Style
Zhang Yue. A Different Method of Solving a Problem of IMO. Int. J. Syst. Sci. Appl. Math. 2020, 5(1), 1-3. doi: 10.11648/j.ijssam.20200501.11
AMA Style
Zhang Yue. A Different Method of Solving a Problem of IMO. Int J Syst Sci Appl Math. 2020;5(1):1-3. doi: 10.11648/j.ijssam.20200501.11
@article{10.11648/j.ijssam.20200501.11, author = {Zhang Yue}, title = {A Different Method of Solving a Problem of IMO}, journal = {International Journal of Systems Science and Applied Mathematics}, volume = {5}, number = {1}, pages = {1-3}, doi = {10.11648/j.ijssam.20200501.11}, url = {https://doi.org/10.11648/j.ijssam.20200501.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20200501.11}, abstract = {The IMO performs once a year, and has become an important activity in the field of mathematics. Because the problems in IMO are very difficult, and in general needs two days to finish the test of only six problems, therefore, it is significant to study how to solve and solve those IMO problems with various methods. With respect to question (a) of the problem of discussing, at first, using the so-called “exhaustive method” and the mathematical induction, the paper gets the conclusion of that if n is the integral multiple of 3, subtracting 1 from the nth power of 2 must be divisible by 7. Furthermore, it also proves by use of the disprove method that if n is not the integral multiple of 3, subtracting 1 from the nth power of 2 is impossible to be divisible by 7. The way of solving question (b) is similar to that of solving (a), in order to use the result of question (a) for the third step of the mathematical induction, the paper firstly consider the third power of that 1 added to (k+1)th power of 2 and applying the disprove method proves that it and hence that 1 added to the (k+1)th power of 2 are not divisible by 7, namely the question (b) is true.}, year = {2020} }
TY - JOUR T1 - A Different Method of Solving a Problem of IMO AU - Zhang Yue Y1 - 2020/04/01 PY - 2020 N1 - https://doi.org/10.11648/j.ijssam.20200501.11 DO - 10.11648/j.ijssam.20200501.11 T2 - International Journal of Systems Science and Applied Mathematics JF - International Journal of Systems Science and Applied Mathematics JO - International Journal of Systems Science and Applied Mathematics SP - 1 EP - 3 PB - Science Publishing Group SN - 2575-5803 UR - https://doi.org/10.11648/j.ijssam.20200501.11 AB - The IMO performs once a year, and has become an important activity in the field of mathematics. Because the problems in IMO are very difficult, and in general needs two days to finish the test of only six problems, therefore, it is significant to study how to solve and solve those IMO problems with various methods. With respect to question (a) of the problem of discussing, at first, using the so-called “exhaustive method” and the mathematical induction, the paper gets the conclusion of that if n is the integral multiple of 3, subtracting 1 from the nth power of 2 must be divisible by 7. Furthermore, it also proves by use of the disprove method that if n is not the integral multiple of 3, subtracting 1 from the nth power of 2 is impossible to be divisible by 7. The way of solving question (b) is similar to that of solving (a), in order to use the result of question (a) for the third step of the mathematical induction, the paper firstly consider the third power of that 1 added to (k+1)th power of 2 and applying the disprove method proves that it and hence that 1 added to the (k+1)th power of 2 are not divisible by 7, namely the question (b) is true. VL - 5 IS - 1 ER -