Let p be a prime number and the set Zp={0,1,2,⋯ ,p−1}\mathbb{Z}_p = \{0,1,2,\cdots,p-1\}Zp={0,1,2,⋯,p−1}. We can map a vector a=⟨a0,a1,a2,⋯ ,ak−1⟩a=\langle a_0,a_1,a_2,\cdots,a_{k-1}\ranglea=⟨a0,a1,a2,⋯,ak−1⟩ into a vector b=⟨b0,b1,b2,⋯ ,bp−1⟩b=\langle b_0,b_1,b_2,\cdots,b_{p-1}\rangleb=⟨b0,b1,b2,⋯,bp−1⟩, where p>k>1p>k>1p>k>1, ai,bi∈Zpa_i,b_i\in\mathbb{Z}_pai,bi∈Zp and bj=∑i=0k−1aiji mod pb_j=\sum_{i=0}^{k-1}a_ij^i \bmod pbj=∑i=0k−1aijimodp, for j=0,…,p−1j=0,\ldots,p-1j=0,…,p−1.
Which of the following statements is/are true?
