If P(x) and Q(x) are two polynomials such that P(x) | P(Q(x)), what could be the conditions for Q such that P...
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If P(x) and Q(x) are two polynomials such that P(x) | P(Q(x)), what could be the conditions for Q such that P (x) = 0 => Q(x) = x?
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If P(x) and Q(x) are two polynomials such that P(x) | P(Q(x)), what are the restrictions for Q such that the statement P (x) = 0 => Q(x) = x to be true (I was thinking the restriction has to be Q to be strictly monotone on Im(Q), but I’m not quite sure)?
If the left to right implication is true, furthermore, can someone please help me prove whether the inverse implication ( If P(x) and Q(x) are two polynomials such that P(x) | P(Q(x)), then Q (x) = x => P (x) = 0 ) holds or is actually false?
abstract-algebra polynomials root-systems
asked Mar 21 at 5:37
Catalin CaldaruseCatalin Caldaruse
61
$endgroup$
add a comment |
$begingroup$
If P(x) and Q(x) are two polynomials such that P(x) | P(Q(x)), what are the restrictions for Q such that the statement P (x) = 0 => Q(x) = x to be true (I was thinking the restriction has to be Q to be strictly monotone on Im(Q), but I’m not quite sure)?
If the left to right implication is true, furthermore, can someone please help me prove whether the inverse implication ( If P(x) and Q(x) are two polynomials such that P(x) | P(Q(x)), then Q (x) = x => P (x) = 0 ) holds or is actually false?
abstract-algebra polynomials root-systems
asked Mar 21 at 5:37
Catalin CaldaruseCatalin Caldaruse
61
$endgroup$
add a comment |
$begingroup$
If P(x) and Q(x) are two polynomials such that P(x) | P(Q(x)), what are the restrictions for Q such that the statement P (x) = 0 => Q(x) = x to be true (I was thinking the restriction has to be Q to be strictly monotone on Im(Q), but I’m not quite sure)?
If the left to right implication is true, furthermore, can someone please help me prove whether the inverse implication ( If P(x) and Q(x) are two polynomials such that P(x) | P(Q(x)), then Q (x) = x => P (x) = 0 ) holds or is actually false?
abstract-algebra polynomials root-systems
asked Mar 21 at 5:37
Catalin CaldaruseCatalin Caldaruse
61
$endgroup$
If P(x) and Q(x) are two polynomials such that P(x) | P(Q(x)), what are the restrictions for Q such that the statement P (x) = 0 => Q(x) = x to be true (I was thinking the restriction has to be Q to be strictly monotone on Im(Q), but I’m not quite sure)?
If the left to right implication is true, furthermore, can someone please help me prove whether the inverse implication ( If P(x) and Q(x) are two polynomials such that P(x) | P(Q(x)), then Q (x) = x => P (x) = 0 ) holds or is actually false?
abstract-algebra polynomials root-systems
abstract-algebra polynomials root-systems
asked Mar 21 at 5:37
Catalin CaldaruseCatalin Caldaruse
61
asked Mar 21 at 5:37
Catalin CaldaruseCatalin Caldaruse
61
asked Mar 21 at 5:37
Catalin CaldaruseCatalin Caldaruse
61
asked Mar 21 at 5:37
Catalin CaldaruseCatalin Caldaruse
61
asked Mar 21 at 5:37
Catalin CaldaruseCatalin Caldaruse
61
61
add a comment |
add a comment |
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