1 | initial version |

What is wrong is the following argument ?

The degree of $phi-phi'$ is d (4 in your example), which is smaller than the degree of h (which is 8 in your example). Hence, $phi-phi' = 0 mod h$ is equivelent to $phi-phi' = 0$. Hence $phi = 0'$ is the only solution to the equation.

2 | No.2 Revision |

What is wrong is the following argument ?

The degree of $phi-phi'$ is ~~d (4 in your example), ~~d, which is smaller than the degree of h ~~(which is 8 in your example). Hence, $phi-phi' = 0 mod h$ is equivelent to $phi-phi' = 0$. Hence $phi = 0'$ is the only solution to the equation.~~since $d<h$. hence,="" $phi-phi'="0" mod="" h$="" is="" equivalent="" to="" $phi-phi'="0$." hence="" $phi="0'$" is="" the="" only="" solution="" to="" the="" equation.<="" p="">

3 | No.3 Revision |

What is wrong is the following argument ?

The degree of $phi-phi'$ is d, which is smaller than the degree of h since $d<h$. hence,="" $phi-phi'="0" mod="" h$="" is="" equivalent="" to="" $phi-phi'="0$." hence="" $phi="0'$" is="" the="" only="" solution="" to="" the="" equation.<="" p="">

4 | No.4 Revision |

What is wrong is the following argument ?

The degree of ~~$phi-phi'$ ~~$\phi-\phi'$ is d, which is smaller than the degree of h since $d<h$. hence,="" ~~$phi-phi'="0" ~~$\phi-\phi'="0" mod="" h$="" is="" equivalent="" to="" ~~$phi-phi'="0$." ~~$\phi-\phi'="0$." hence="" ~~$phi="0'$" ~~$\phi="0'$" is="" the="" only="" solution="" to="" the="" equation.<="" p="">

5 | No.5 Revision |

What is wrong is the following argument ?

The degree of $\phi-\phi'$ is d, which is smaller than the degree of h since $d<h$. hence,="" $\phi-\phi'="0" mod="" h$="" is="" equivalent="" to="" $\phi-\phi'="0$." hence="" $\phi="0'$" is="" the="" only="" solution="" to="" the="" equation.<="" p="">

6 | No.6 Revision |

What is wrong is the following argument ?

The degree of $\phi-\phi'$ is d, which is smaller than the degree of h since ~~$d<h$. ~~$d<h$ .="" hence,="" $\phi-\phi'="0" mod="" h$="" is="" equivalent="" to="" $\phi-\phi'="0$." hence="" $\phi="0'$" is="" the="" only="" solution="" to="" the="" equation.<="" p="">

7 | No.7 Revision |

What is wrong is the following argument ?

The degree of $\phi-\phi'$ is d, which is smaller than the degree of h since $d<h$ ~~.="" hence,="" $\phi-\phi'="0" mod="" h$="" is="" equivalent="" to="" $\phi-\phi'="0$." hence="" $\phi="0'$" is="" the="" only="" solution="" to="" the="" equation.<="" ~~.<="" p="">

Hence, $\phi-\phi' = 0 \mod h$ is equivalent to $\phi-\phi' = 0$. Hence $\phi = 0'$ is the only solution to the equation.

8 | No.8 Revision |

What is wrong is the following argument ?

The degree of $\phi-\phi'$ is d, which is smaller than the degree of h since $d<h$ .<="" p="">

Hence, $\phi-\phi' = 0 \mod h$ is equivalent to $\phi-\phi' = 0$. Hence $\phi = ~~0'$ ~~0$ is the only solution to the equation.

9 | No.9 Revision |

What is wrong is the following argument ?

The degree of $\phi-\phi'$ is d, which is smaller than the degree of h since ~~$d<h$ .<="" ~~$d<h$.< p="">

Hence, $\phi-\phi' = 0 \mod h$ is equivalent to $\phi-\phi' = 0$. Hence $\phi = 0$ is the only solution to the equation.

10 | No.10 Revision |

What is wrong is the following argument ?

The degree of $\phi-\phi'$ is d, which is smaller than the degree of h since ~~$d<h$.< ~~$d<h$< p="">

Hence, $\phi-\phi' = 0 \mod h$ is equivalent to $\phi-\phi' = 0$. Hence $\phi = 0$ is the only solution to the equation.

11 | No.11 Revision |

What is wrong is the following argument ?

The degree of $\phi-\phi'$ is d, which is smaller than the degree of h since ~~$d<h$< ~~$d<h$ <="" p="">

Hence, $\phi-\phi' = 0 \mod h$ is equivalent to $\phi-\phi' = 0$. Hence $\phi = 0$ is the only solution to the equation.

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.